A bakery sells rolls in units of a dozen. The demand X (in 1000 units) for rolls has a gamma distribution with parameters α = 3, θ = 0.5, where θ is in units of days per 1000 units of rolls. It costs $ 2 to make a unit that sells for $ 5 on the first day when the rolls are fresh. Any leftover units are sold on the second day for $ 1. How many units should be made to maximize the expected value of the profit?

Answers

Answer 1

Answer:

The value  is  [tex]E(X) =  \$ 1.7067 [/tex]

Step-by-step explanation:

From the question we are told that

   The  parameters  are  α = 3, θ = 0.5

    The cost of making a unit on the first day  is  c = $2

    The selling price of a  unit on the first day is  s = $5

    The selling price of a leftover unit on the second day is  v  = $ 1

Generally the profit of a unit on the first day is

        [tex]p_1 = 5 - 2[/tex]

           [tex]p_1 = \$3 [/tex]

The profit of a unit on the second day is

       [tex]p_2 = 1 - 2[/tex]

=>     [tex]p_2 = - \$1 [/tex]

Generally the probability of making profit greater than $ 1 is mathematically represented as

    [tex]P(X >  1 ) = Gamma (X ,\alpha , \theta)[/tex]

=>   [tex]P(X >  1 ) = Gamma (1 ,3 , 0.5)[/tex]

Now from the gamma distribution table  we have that

    [tex]P(X >  1 ) =  0.67668[/tex]

Generally the probability of making profit less than or  equal to  $ 1 is mathematically represented as

       [tex] P(X \le  1 ) = 1 - P(X >  1 )[/tex]

=>     [tex] P(X \le  1 ) = 1 - 0.67668[/tex]

=>     [tex] P(X \le  1 ) = 0.32332[/tex]    

So  the probability of making  $3  is    [tex]P(X >  1 ) =  0.67668[/tex]

and  the probability of making  -$1  is   [tex] P(X \le  1 ) = 0.32332[/tex]  

Generally the value of profit per day is mathematically represented as

      [tex]E(X) =  3 *  P(X >  1 )   +   (-1  *  P(X \le 1 ) )[/tex]

=>     [tex]E(X) =  3 * 0.67668   +   (-1  *  0.32332 )[/tex]

=>     [tex]E(X) =  \$ 1.7067 [/tex]


Related Questions

Pls answer i will mark u brainlist

Answers

Answer:

See below.

Step-by-step explanation:

Given :-

Length = 10 mBreadth = 5 mHeight = 12 mCost of white washing = ₹7 per m²

To Find :-

cost of washing 4 wallscost if ceiling is also washed

Solving :-

Step 1 : Find the area of 4 walls

Area = 2 x 12(10 + 5)Area = 24 x 15Area = 360 m²

Step 2: Cost for 4 walls

Cost = 360 x 7Cost = ₹2520

Step 3: Find Area of Ceiling

Area = 10 x 5 = 50 m²Total area = 360 + 50 = 410 m²

Step 4: Total Cost

Cost = 410 x 7Cost = ₹2870

Given↷

Length of the room⇢ 10m

Height of the room⇢12m

width of the room⇢5m

Cost of white washing a m²⇢₹7

To find↷

the total cost of white washing of 4 walls + the ceiling of the room

Answer↷

₹2,870

Solution↷

To find the total cost of white washing of 4 walls + the ceiling of the room ,

we'll find the lateral surface area of the room & the area of the ceilings then add them up and multiply the answer by 7

Lateral surface area ⇢2h(l + w)Area ⇢l x w

Lateral surface area of the room

⤿ 2 x 12m(10m+5m)

⤿2 x 180m²

⤿360m²

Area of the ceilings

⤿ 10m x 5m

⤿50m²

Cost of white washing 4 walls + the ceiling

⤿ ₹7(360m²+50m²)

⤿₹7 x 410m²

⤿₹ 2,870

4. Three times the sum of 2 and the number of points Robbie scored in
his last basketball game is at least 36. What are possible numbers of
points Robbie scored?

Answers

Answer:

6

Step-by-step explanation:

if times come in any word problem it means we have to multiply so here you have to multiple 3

suppose here any number if x and question says sum of 2 so

3(x+x)=36

3(2x)=36

6x=36

so x=6

Which number line below correctly represents the expression -3 + 4?

Answers

Answer:

1st answer

Step-by-step explanation:

First you subrtract 3 from 0 then add 4 to -3

10 Which number comes between
74.97 and 16.08?
A. 14.79
B. 16.09
C. 16.1
D. 15.543

Answers

I am going to assume this a typo (14.97), so the answer would be D.

If not, both B and C fall between those numbers.

SOMEONE HELP ASAP Ill give brainist and 100 points

Answers

Answer:

x=0

Step-by-step explanation:

the axis of symmetry is 0

Heyo Brother!

It's me Violet! ^w^

I could be wrong.. but, I believe the answer is..

[tex](0,20)[/tex]

Hopefully, this helps chu!

:3

Have a awesome day~

[tex]XxVioletXx[/tex]

what is the ratio of students who dance to total number of students 35,27,43,33,26

Answers

Answer:

The true statements are :

A. assertEquals(student1,student2)

C. assertSame(student1,student3)

Explanation:

AssertEquals() asserts that the objects are equal, but assertSame() asserts that the passed two objects refer to the same object or not, if found same they return true, else return false.

i hope this work for you

write 3x-9y=36 using function notation then find f(-15)

Answers

Answer:

1

Step-by-step explanation:

3x-9y=36

9y = 3x - 36

y = 3/9x - 36/9

F(x) = 1/3x - 4

F(-15) = (15/3) - 4 = 5 - 4 = 1

9) which is 16/6 as a decimal?
0.375
2.67
10
3

Answers

Answer:

2.67 is the answer

Step-by-step explanation:

use symbolab I use it all the time

Which point has coordinates (–5, 8)?

Answers

Answer:

I don't know this but when I do I'll tell you :))

Step-by-step explanation:

hello people ~
Sketch the graph of y = 4 cos 3x° + 7

Answers

Answer:

[tex]\sf\fbox\red{Answer:-}[/tex]

The answer in the attachment may help uh

[tex]\small\fbox{\blue{\underline{mαrk \; mє \; вrαínlíєѕt \; plєαѕє ♥}}}[/tex]

[tex]\sf \bold{\:y\:=\:4\:cos\:3x\:+\:7}[/tex]

[tex]\sf \sf{Y\:Intercepts}:\:\left(0,\:11\right)[/tex][tex]\sf \sf{X\:Intercepts}:\:\left none[/tex][tex]\sf \sf \sf{Asymptotes}:\:\left none[/tex][tex]\sf \sf{Domain}:\:\left(-\infty \: < x < \infty )[/tex]

graph attached below:

[ fieryanswererft ]

If ST=w–47 and RU=w–63, what is the value of w?

Answers

Answer:

w = 79

Step-by-step explanation:

We know that RU us a midsegment so it must be 1/2 of ST.

So ST = 2RU.

w-47 = 2(w-63)

w-47 = 2w-126

-w = -79

w = 79

PLS PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS

Answers

Answer:

-2, 9

Step-by-step explanation:

find the value of k if: (2x − y) 2 − (2x + y) 2 = 4xyk

Answers

(2x−y)(2)−(2x+y)(2)=4xyk

4kxy = -4y

4kxy/4xy = -4/4xy

k = -1/x

Please Help me with Steps I really need to understand and this

Answers

Answer:

75 cm³

Step-by-step explanation:

the volume formula of an irregular object is length*width*height

the length of this would be 5 cm the height is 4 cm and the width is 3 cm so using the l*w*h the answer is 60 cm and the next one should be 15 since 1*3*5 is 15 add those together to get 75 cm³

Pleaseeee help asappppppp

Answers

Answer:

ED = 12

HOPE THIS HELP YOU , FOR ANY QUESTION PLEASE ASK ME .

3 The table shows Clark's assets and liabilities.
What is Clark's net worth?
Item
Cash/Savings
Credit Card Debt
Car Payoff
Clothes
Student Loan
Value ($)
375
3,405
2,645
525
1,366
OH $5,150
F -$6,516
G-$5,150
O , $6,516

Answers

Clark's net worth given his assets and liabilities is $-6516.

What is Clark's net worth?

Net worth is total assets less liabilities. Assets are items owned by a person that creates benefits in the future to the person. Clark's assets are cash and clothes.

Liabilities are what are owed to another person. They reduce the economic value of a person. Clark's liabilities are credit card debt, car pyoff and student loan.

Net worth = 375 - 3405 - 2645 + 525 - 1366 = $-6,516.

To learn more about net worth, please check: https://brainly.com/question/13733365

What is 13.035 rounded to the nearest hundredth

Answers

Answer:13.04

Step-by-step explanation:

in the xy plane, if a point with coordinated (a,b) lies in the soution set of the system of inequalities above, what is the maximum possible value of b y ≤ -15x + 300​
PLEASE HELP IM BROKE ON POINTS

Answers

Answer:

Another equation is missing. Can't solve for b with just one equation

If 4 snow cones cost $14, how much do 3 snow cones cost?

Answers

$10.50

14÷4= 3.5 so, 3.5 x 3 = 10.50

We found in the previous task, that Chef Walton cooked 50 meals first. However, for the next dinner service, Chef Barber prepared 14 meals ahead of time, instead of 7. What will be the effect of Chef Barber's new initial value? Check all that apply.

Answers

Answer:

Chef Barber will now cook 50 meals first and The new y-intercept will change the result.

Step-by-step explanation:

I just did on edge

Given question is incomplete without options and the information regarding the cooking of two chefs; Find the compete question in attachment.

Options for the question are,

A). Chef Walton will still cook 50 meals first.

B). Chef Barber will now cook 50 meals first.

C). The new y-intercept will have no effect.

D). The new y-intercept will change the results.

Options B and D are the correct options.

    Given in the question,

Chef Walton cooked 50 meals first.Chef Barber prepared 14 meals ahead of time, instead of 7.

From the picture attached,

Chef Barber prepared 7 meals before the dinner and must prepare 13 meals per hour during dinner.

       So the equation for the total meals 'y' prepared in 'x' hours by chef

       Barber will be,

       y = 13x + 7

       Therefore, duration for 50 meals to be prepared,

       50 = 13x + 7

      x = 3.62 hours

       If Chef Barber prepared 14 meals before dinner service,

       Equation for the meals prepared will change to,

      y = 13x + 14

       New time to prepare for 50 meals,

       50 = 13x + 14

       x = 2.77 hours        

    2. From the graph given in the picture,

        Slope of the line between two points (0, 4) and (3, 49),

        m = [tex]\frac{49-4}{3-0}[/tex]

        m = 15

        Here, slope of the line defines number of dishes prepared per hour by

        Chef Walton.

        Chef Walton prepared 4 dishes before the dinner service,

        y = 15x + 4

        Time taken to prepare 50 meals,

        50 = 15x + 4

        x = 3.07 hours

Now check the options given,

Option A

"Chef Walton will still cook 50 meals first.

Since, new time taken by Chef Barber (2.77 hours) is less than the time taken by Chef Walton (3.07 hours),

Option A is false.

Option B

"Chef Barber will now cook 50 meals first"

True.

Option C

"The new y-intercept will have no effect"

False.

Option D

"The new y-intercept will change the results"

True.

    Therefore, Options B and D will be correct.

Learn more,

https://brainly.com/question/25276357?

A company that uses job order costing reports the following information. Overhead is applied at the rate of 60% of direct materials. The company has no beginning Work in Process or Finished Goods inventories. Jobs 1 and 3 are not finished by the end of March, and Job 2 is finished but not sold by the end of March

Answers

Based on the percentage completed and the cost of the jobs, total value of work in process inventory at the end of March is $62,480.

What is the Work in Process Inventory?

The work in process will include Jobs 1 and 3 only because job 2 is already done.

Work in process can be found as:

= Cost of job 1 + Cost of job 3

Cost of a single job is:

= Direct labor + Direct materials + Overhead which is 60% of direct materials

Solving for both jobs gives:

= (13,400 + 21,400 + (13,400 x 60%)) + (6,400 + 9,400 + (6,400 x 60%))

= $62,480

Find out more on Work in Process at https://brainly.com/question/7932472.

Select the correct answer.
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
cd4
c2d8
A cd4
ООО
OB.
Oc.
ca2
1
ca4
OD.cd2

Answers

Answer: D. 1/cd^4 (simplified)

5+(-12)-(-7)=
simplify

Answers

Answer:

0

Step-by-step explanation:

First add -12 + 7 then 5+ -5

Please choose 1 2 or 3 will mark Brainlist

Answers

it's,

HHH, TTT, HTT

Step-by-step explanation:

If 3 coins are tossed, then the possible sample space can be : HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

where H=heads,T=tails

What is the answer? (Geometry)

Answers

Answer:

[tex]\angle {1} = 90\\\angle {2} = 45\\\angle {3} =55[/tex]

Step-by-step explanation:

1 is 90 because it's placed onto a straight line the equals 180 degrees, therefore it's 90 because the other 2 angles with it are the same, meaning that they had to be 45. 3 is 55 because 90+35=125, and the sum of all 3 angles in a triangle must equal 180, therefore 180-125=55.

Deshaun rented a truck for one day. There was a base fee of $16.95, and there was an additional charge of 84 cents for each mile driven. Deshaun had to pay $237.03 when he returned the truck. For how many miles did he drive the truck?

Answers

Subtract the rental fee from the total:

237.03 - 16.95 = 220.08

Now divide the remainder by the charge per mile:

220.08 / 0.84 = 262

He drove 262 miles.

Faith started last week with $1,100 in her checking account. During the week, she wrote the checks below.
On the 15th, Faith received a paycheck for $583.67. She recorded all of these transactions in her checking
Account Number: 1234-1212
Checks date check no. amount
9/5 241 $67.25
9/20 242 $36.80
9/30 243 $15.00
Other Activity date transaction amount
9/30 Deposit $650.45
9/30 Fees $15.00
Balances Opening Balance $900.00
Closing Balance $1,416.40




A.
His check to the barber shop was not cashed before the end of the month.
B.
He added up his transactions incorrectly.
C.
He mislabeled a payment as a deposit.
D.
He had bank fees that were not in his check register.

Any help would be appreciated thanks!!

Answers

Answer:

B.

He added up his transactions incorrectly.

Please help me quick this is for today my math grade is already a 61!

Answers

Answer:

Dude my answer got  deleted for no reason!

Step-by-step explanation:

Answer:

a,c,d and maybe e

Step-by-step explanation:

sorry if im wrong

There is 885 mL of milk in one jug and 550 mL in another. How much milk is there both the jugs?

Answers

Answer:

1,435 mL

Step-by-step explanation:

This is a simple addition problem if I'm not mistaken.

885+550=1435

is it a or c ? im ot sure

Answers

Answer:

NEVER MIND A IS CORRECT

Step-by-step explanation:

160 of 72 % is 115.2

but in total it is of 222.2

Answer:

its A

Step-by-step explanation:

222.2

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