Question

D. 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? Please use Excel and include all formulas used.

Answer 1

Using the given P2 and P1 we get the sales, then the profit for each scenario, then the expected profit.

Step 1	Sale units	PK Price	7	8	9	10	11	Step 2	Profit	PK Price	7	8	9	10	11	Step 3	Expected profit	PK Price	7	8	9	10	11
	Probability	NG Price							Probability	NG Price							Probability	NG Price
	0.3	8	125	100	75	50	25		0.3	8	125	200	225	200	125		0.3	8	37.50	60.00	67.50	60.00	37.50
	0.5	10	175	150	125	100	75		0.5	10	175	300	375	400	375		0.5	10	87.50	150.00	187.50	200.00	187.50
	0.2	12	225	200	175	150	125		0.2	12	225	400	525	600	625		0.2	12	45.00	80.00	105.00	120.00	125.00
																		Total	170.00	290.00	360.00	380.00	350.00

So total expected profit is max at Pk price at $10

So it should be charged.

The formulae used:

Step 1

Sale units

PK Price

7

8

9

10

11

Step 2

Profit

PK Price

7

8

9

10

11

Step 3

Expected profit

PK Price

7

8

9

10

11

Probability

NG Price

Probability

NG Price

Probability

NG Price

0.3

8

=100+25*($C3-D$1)

=100+25*($C3-E$1)

=100+25*($C3-F$1)

=100+25*($C3-G$1)

=100+25*($C3-H$1)

0.3

8

=D3*(L$1-6)

=E3*(M$1-6)

=F3*(N$1-6)

=G3*(O$1-6)

=H3*(P$1-6)

0.3

8

=$R3*L3

=$R3*M3

=$R3*N3

=$R3*O3

=$R3*P3

0.5

10

=100+25*($C4-D$1)

=100+25*($C4-E$1)

=100+25*($C4-F$1)

=100+25*($C4-G$1)

=100+25*($C4-H$1)

0.5

10

=D4*(L$1-6)

=E4*(M$1-6)

=F4*(N$1-6)

=G4*(O$1-6)

=H4*(P$1-6)

0.5

10

=$R4*L4

=$R4*M4

=$R4*N4

=$R4*O4

=$R4*P4

0.2

12

=100+25*($C5-D$1)

=100+25*($C5-E$1)

=100+25*($C5-F$1)

=100+25*($C5-G$1)

=100+25*($C5-H$1)

0.2

12

=D5*(L$1-6)

=E5*(M$1-6)

=F5*(N$1-6)

=G5*(O$1-6)

=H5*(P$1-6)

0.2

12

=$R5*L5

=$R5*M5

=$R5*N5

=$R5*O5

=$R5*P5

Total

=SUM(T3:T5)

=SUM(U3:U5)

=SUM(V3:V5)

=SUM(W3:W5)

=SUM(X3:X5)