Question

Seved Help Save & Exit Submit Famous Albert prides himself on being the Cookie King of the West. Small, freshly baked cookies are the specialty of his shop. Famous Albert has asked for help to determine the number of cookies he should make each day. From an analysis of past demand, he estimates demand for cookies as DEMAND 2,808 dezen 2,200 2,400 2,600 2,800 3, bee 3,200 PROBABILITY OF DEMAND 0.03 0.10 0.29 0.30 0.14 e.es 2.09 Each dozen sells for $0.66 and costs $0.48, which includes handling and transportation. Cookies that are not sold at the end of the day are reduced to $0.27 and sold the following day as day-old merchandise. a. Compute the expected profit or loss for each cookie making decision quantity. (Round your answer to the nearest whole number. Enter expected losses with a negative sign.) Expected Profit/Loss Cookies Baked (Dozen) 2,000 2,200 Probability of Demand 0.03 0.10 < Prev 6 of 15 Next > e 700 O Search

Answer 1

Given,

Selling Price = $0.66 per dozen

Cost price = $0.48 per dozen

Salvage value = $0.27 per dozen

Marginal Profit,p = Selling price - Cost price = 0.66 - 0.48 = $0.18 per dozen

Marginal loss,l = cost price - Salvage value = 0.48 - 0.27 = $0.21 per dozen

In the below table,

If Demand = Production, Total Profit = Number of dozens * p

If Demand > Production, profit = Number of dozens in production * p

If demand < Production, profit = Number of dozens in Production *p - (Extra dozens * l )

2600 Demand Probability Production 2000 2000 0.03 2200 0.1 2400 0.29 2800 0.14 3000 0.05 0.3 360 360 360 360 360 360 3200 Expected Value (sum 0.09 of (Each value *prob) 360 360 396 393.66 432 419.52 468 422.76 2200 318 396 396 396 396 432 2400 396 354 312 276 432 432 390 432 468 2600 234 468 468 426 2800 192 270 348 504 504 504 402.6 3000 150 228 306 384 462 540 540 371.52 3200 108 186 264 342 420 498 576 336.54

b.

From the table,

Profit is maximum at 2600 dozen of production ,

Hence,

Optimal Production = 2600 dozens

Optimal profit = $422.76

c.

In the marginal analysis,

P < 1 / (1+p)

P < 0.21 / (0.21 + 0.18)

P < 0.21 / 0.39

P < 0.5384

Hence,

Probability should be less than 0.5384

Table for cumulative probabilities is given below:

Cookies Baked (Dozen)	Probability of Demand	Cumulative Probability
2000	0.03	0.03
2200	0.1	0.13
2400	0.29	0.42
2600	0.3	0.72
2800	0.14	0.86
3000	0.05	0.91
3200	0.09	1

At 2400,

P = 0.42 < 0.5384

Hence,

Optimal Quantity is 2400,

Expected Profit will be $419.52.