Question

Pizza King (PK) and Noble Greek (NG) are competitive pizza chains. PK believes there is a 30% chance that NG will charge $8 per pizza, a 50% that NG will charge $10 per pizza, and a 20% chance that NG will charge $12 per pizza. If PK charges price p1 and NG charges price p2, PK will sell 100 + 25(p2 – p1) pizzas. It costs PK $6 to make a pizza. PK is considering charging $7, $8, $9, $10, or $11 per pizza. To maximize its expected profit, what price should PK charge for a pizza?

Answer 1

Price of Pizza of NK = SUMPRODUCT of probability*value = 30%*8 + 50%*10 20%*12 = 9.8$

Number of Pizza sold by PK = 100 + 25*(9.8-P1)

Profit = Number of Pizza sold*(P1-6) = (345 - 25*P1)*(P1-6)

Using hit and trial for each value of P1

At P1 =7, Profit is (345-25*7)*(7-6) = 170

At P1 =8, Profit is (345-25*8)*(8-6) = 290

At P1 =9, Profit is (345-25*9)*(9-6) = 360

At P1 =10, Profit is (345-25*10)*(10-6) = 380

At P1 =11, Profit is (345-25*11)*(11-6) = 350

Ans: 10 $