Question

A chef must decide how many chocolate lava cakes to prepare for the upcoming Mother's Day Dinner special. The chef can either prepare 50, 100, or 150 lava cakes. Assume that demand for the surf and turf can be 50, 100, or 150.

Each dish costs $5 to make and is priced at for $7 on the menu. Unsold cakes are donated to a nearby charity center. Assume that there is no opportunity cost for lost sales.

1. Which alternative should be chosen based on the maximax criterion?

2. Which alternative should be chosen based on the minimax regret criterion?

3. What is the best alternative using the EMV criterion? Given: The cafe owner told the chef that in the past years, the probability that clients will order 50 cakes is 0.30; the probability they will order 100 cakes is 0.50, and the probability that they will order 150 cakes is 0.20.

Answer 1

Let P and D be the number of Cakes prepared and demanded respectively.

For D > P, Profit = (7 - 5) * P = 2P

For P > D, Profit = 7D - 5P

The Payoff table is,

Demand	50	100	150
Prepare 50 cakes	2 * 50 = 100	2 * 50 = 100	2 * 50 = 100
Prepare 100 cakes	7 * 50 - 5 * 100 = -150	2 * 100 = 200	2 * 100 = 200
Prepare 150 cakes	7 * 50 - 5 * 150 = -400	7 * 100 - 5 * 150 = -50	2 * 150 = 300

1.

Maximum profit for Prepare 50 cakes is $100

Maximum profit for Prepare 100 cakes is $200

Maximum profit for Prepare 150 cakes is $300

The maximum of all maximum profits is $300 which is for Prepare 150 cakes .

Prepare 150 cakes should be chosen based on the maximax criterion.

2.

Regret = Maximum Payoff - Pay off received

Demand	50	100	150
Prepare 50 cakes	100-100 = 0	200 - 100 = 100	300 - 100 = 200
Prepare 100 cakes	100 - (-150) = 250	200 - 200 = 0	300 - 200 = 100
Prepare 150 cakes	100 - (-400) = 500	200 - (-50) = 250	300 - 300 = 0

Maximum regret for Prepare 50 cakes is $200

Maximum regret for Prepare 100 cakes is $250

Maximum regret for Prepare 150 cakes is $500

The minimum of all maximum regret is $200 which is for Prepare 50 cakes .

Prepare 50 cakes should be chosen based on the minimax regret criterion.

3.

EMV for Prepare 50 cakes = 100 * 0.30 + 100 * 0.50 + 100 * 0.20 = 100

EMV for Prepare 100 cakes = -150 * 0.30 + 200 * 0.50 + 200 * 0.20 = 95

EMV for Prepare 150 cakes = -400 * 0.30 - 50 * 0.50 + 300 * 0.20 = -85

The maximum of EMV is $100 which is for Prepare 50 cakes .

Prepare 50 cakes should be chosen using the EMV criterion.