The Camera Shop sells two popular models of digital SLR cameras. The sales of th

ID: 3057540 • Letter: T

Question

The Camera Shop sells two popular models of digital SLR cameras. The sales of these products are not independent; if the price of one increases the sales of the other increases. In economics, these two camera models are called substitutable products. The store wishes to establish a pricing policy to maximize revenue from these products. A study of price and sales data shows the following relationships between the quantities sold (N) and price (P) of each model: NA = 195-0.6Pa + 0.25Pa Na = 301 + 0.08P,-0.5PB 1a. Construct a model for the total revenue and implement it on a spreadsheet (6 pts) 1b. Develop a 2-way data table to estimate to optimal prices for each product in order to maximize the total revenue. Vary each price from $250 to $500 in increments of $10. Identify the optimal prices and associated total revenue. (6 pts)

Explanation / Answer

Part (a)

Given NA = 195 – 0.6PA + 0.25PB and NB = 301 + 0.08PA - 0.5PB, total revenue, R is given by:

R = (NA x PA) + (NB x PB).

On substituting given equations and simplifying,

R = 195PA – 0.6PA2 + 301PB - 0.5PB2 + (0.33 x PA x PB) ANSWER

Part (b)

Part of Excel output is given below.

The value of R for various combinations of PA and PB are given by: a3 + b3 + 0.33(PA x PB)

As can be seen from the table, for a fixed PB, R keeps decreasing as PA increases implying the maximum R occurs at PA = 250.

Now, at PA = 250, R keeps increasing up to PB = 380 and then R keeps decreasing imp;ying that R is maximum at PA = 250 and PB = 380 and the maximum R is $84780. ANSWER

b1 = 301PB

b2 = 0.5PB^2

b3 = b1 - b2

250

260

270

280

290

300

a1 = 195PA

48,750

50,700

52,650

54,600

56,550

58,500

a2 = 0.6PA^2

37,500

40,560

43,740

47,040

50,460

54,000

a3 = a1 - a2

11,250

10,140

8,910

7,560

6,090

4,500

250

75250

31250

44000

75,875

75,590

75,185

74,660

74,015

73,250

260

78260

33800

44460

77,160

76,908

76,536

76,044

75,432

74,700

270

81270

36450

44820

78,345

280

84280

39200

45080

79,430

290

87290

42050

45240

80,415

300

90300

45000

45300

81,300

310

93310

48050

45260

82,085

320

96320

51200

45120

82,770

330

99330

54450

44880

83,355

340

102340

57800

44540

83,840

350

105350

61250

44100

84,225

360

108360

64800

43560

84,510

370

111370

68450

42920

84,695

380

114380

72200

42180

84,780

390

117390

76050

41340

84,765

400

120400

80000

40400

84,650

410

123410

84050

39360

84,435

420

126420

88200

38220

84,120

430

129430

92450

36980

83,705

440

132440

96800

35640

83,190

450

135450

101250

34200

82,575