Question

The bookstore sells promotional booklets. You can buy the booklets from your supplier in bundles of one dozen each. Each booklet in the bundle costs $65, and will sell for $90. Booklets unsold by specific event will be clearance priced at $20. The bookstore estimates that demand patterns will follow the table below. How many bundles should be purchased based on EMV criteria?

Demand level	Probability
1 bundle	10 percent
2 bundles	30 percent
3 bundles	50 percent
4 bundles	10 percent

Answer 1

Profit =Selling Price - Cost Price =(90*12) - (65*12) =1080 - 780 =300

Loss =Cost Price - Clearance Price =(65*12) - (20*12) =780 - 240 =540

Pay-off table:

Demand/Supply	A1: 1bundle	A2: 2 bundles	A3: 3 bundles	A4: 4 bundles
1 bundle	300	300 - 540 = -240	300 - 2(540) =300 - 1080 = -780	300 - 3(540) =300 - 1620 = -1320
2 bundles	300	2*300 =600	600 - 540 =60	600 - 2(540) =600 - 1080 = -480
3 bundles	300	600	3*300 =900	900 - 540 =360
4 bundles	300	600	900	4*300 =1200

(A1, A2, A3 and A4 are four different alternatives of supply).

For A2:

When the supply is 2 bundles and the demand is more than 2 bundles, i.e., 3 or 4 bundles, then only 2 bundles can be sold and profit is the same 600 for the demand of 3 and 4 bundles (there are no unsold bundles).

For A2:

When the supply is 2 bundles and the demand is only for 1 bundle and so, 1 bundle is sold for a profit of 300 but 1 bundle is left unsold which is cleared with a loss of 540. So, the payoff =300 - 540 = -240 (i.e., loss of $240).

This explaination can be applied to the remaining payoffs.

Expected Monetary Value, EMV =(Pay-off*Probability)

EMV table:

Demand/Supply	Probability	A1 : 1 bundle	A2: 2 bundles	A3: 3 bundles	A4: 4bundles
1 bundle	0.10	300*0.10 =30	-240*0.10 = -24	-780*0.10 = -78	-1320*0.10 = -132
2 bundles	0.30	300*0.30 =90	600*0.30 =180	60*0.30 =18	-480*0.30 = -144
3 bundles	0.50	300*0.50 =150	600*0.50 =300	900*0.50 =450	360*0.50 =180
4 bundles	0.10	300*0.10 =30	600*0.10 =60	900*0.10 =90	1200*0.10 =120
Total	1	300	516	480	24

EMV in case of A2 is greater than the remaining alternatives of supply. Thus, it is recommended to have a supply of 2 bundles where EMV =$516.

Therefore, 2 bundles should be purchased based on EMV criteria.