Question

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		PROBABILITY OF DEMAND
1,800	dozen	0.05
2,000		0.08
2,200		0.29
2,400		0.28
2,600		0.13
2,800		0.04
3,000		0.13

Each dozen sells for $0.69 and costs $0.46, which includes handling and transportation. Cookies that are not sold at the end of the day are reduced to $0.29 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.)

	Cookies Baked (Dozen) Probability of Demand Expected Profit/Loss 1,800 0.05 2,000 0.08 2,200 0.29 2,400 0.28 2,600 0.13 2,800 0.04 3,000 0.13

b. Based on your answers to part a., what is the optimal number of cookies to make?

c. By using marginal analysis, what is the optimal number of cookies to make?

Answer 1

Ans a	Profitability
Highest profitability is to make 2400 doz cookies	$                504.00
Ans b optimal number of cookies to make	2400	dozen
Ans c :	2400	dozen
the marginal analysis shows the probability of demand increases to .58 when demand is 2400 doz cookies, profit increase till output is 2400 doz then declines. (Refer attached chart)

Selling Price of a dozen	$                     0.69
Cost price of a dozen	$                     0.46
Salvage price of a dozen	$                     0.29
Demand	Probability of Demand	Cumulative demand (probability of selling n th unit)	Expected number sold	unsold quantity	sold	unsold	cost	total revenue	Expected profit/ loss
a	b		c=2000*.95+1800*.05	d'=a-c	e=a*.69	f=d*.29	g=a*.46	h=e+f	=h-g
1800	0.05	1	1800	0	$       1,242	$            -	$        828.00	$             1,242	$                 414.00
2000	0.08	0.95	1990	10	$       1,373	$        2.90	$        920.00	$             1,376	$                 456.00
2200	0.29	0.87	2164	36	$       1,493	$     10.44	$    1,012.00	$             1,504	$                 491.60
2400	0.28	0.58	2280	120	$       1,573	$     34.80	$    1,104.00	$             1,608	$                 504.00
2600	0.13	0.3	2340	260	$       1,615	$     75.40	$    1,196.00	$             1,690	$                 494.00
2800	0.04	0.17	2374	426	$       1,638	$   123.54	$    1,288.00	$             1,762	$                 473.60
3000	0.13	0.13	2400	600	$       1,656	$   174.00	$    1,380.00	$             1,830	$                 450.00

Formulas:

Selling Price of a dozen	0.69
Cost price of a dozen	0.46
Salvage price of a dozen	0.29

Demand	Probability of Demand	Cumulative demand (probability of selling n th unit)	Expected number sold	unsold quantity	sold	unsold	cost	total revenue	Expected profit/ loss
a	b		c=2000*.95+1800*.05	d'=a-c	e=a*.69	f=d*.29	g=a*.46	h=e+f	=h-g
1800	0.05	1	=A7*C7	=A7-D7	=D7*$B$1	=E7*$B$3	=A7*$B$2	=F7+G7	=I7-H7
2000	0.08	=C7-B7	=A8*C8+A7*B7	=A8-D8	=D8*$B$1	=E8*$B$3	=A8*$B$2	=F8+G8	=I8-H8
2200	0.29	=C8-B8	=A9*C9+A8*B8+A7*B7	=A9-D9	=D9*$B$1	=E9*$B$3	=A9*$B$2	=F9+G9	=I9-H9
2400	0.28	=C9-B9	=C10*A10+B9*A9+B8*A8+B7*A7	=A10-D10	=D10*$B$1	=E10*$B$3	=A10*$B$2	=F10+G10	=I10-H10
2600	0.13	=C10-B10	=A11*C11+A10*B10+A9*B9+A8*B8+A7*B7	=A11-D11	=D11*$B$1	=E11*$B$3	=A11*$B$2	=F11+G11	=I11-H11
2800	0.04	=C11-B11	=A12*C12+A11*B11+A10*B10+A9*B9+A8*B8+A7*B7	=A12-D12	=D12*$B$1	=E12*$B$3	=A12*$B$2	=F12+G12	=I12-H12
3000	0.13	=C12-B12	=A13*C13+A12*B12+A11*B11+A10*B10+A9*B9+A8*B8+A7*B7	=A13-D13	=D13*$B$1	=E13*$B$3	=A13*$B$2	=F13+G13	=I13-H13