Jim's Camera shop sells two high-end cameras, the Sky Eagle and the Horizon. The demand for these two cameras are as follows: D_S = demand for the Sky Eagle, P_S is the selling price of the Sky Eagle, D_H is the demand for the Horizon, and P_H is the selling price of the Horizon.

D_S = 206 - 0.61P_S + 0.59P_H

D_H = 271 + 0.23P_S - 0.51P_H

The store wishes to determine the selling price that maximizes revenue for these two products. Develop the revenue function for these two models. Enter negative answers as positive values.

P_SD_S + P_HD_H = P_S (fill in the blank 1 - fill in the blank 2P_S + fill in the blank 3P_H) + P_H (fill in the blank 4 + fill in the blank 5P_S - fill in the blank 6P_H)

Find the revenue maximizing prices. Round your answers to the nearest cent.

Revenue: $  fill in the blank 7

Revenue Function is given by -

PSDS + PHDH = PS * (206 - 0.61PS + 0.59PH) + PH * (271 + 0.23PS - 0.51PH)

Comparing the above equation with below given equation

PS*DS + PH*DH = PS (fill in the blank 1 - fill in the blank 2 PS + fill in the blank 3 PH) + PH (fill in the blank 4 + fill in the blank 5 PS - fill in the blank 6 PH)

We get -

fill in the blank 1 = 206

fill in the blank 2 = 0.61

fill in the blank 3 = 0.59

fill in the blank 4 = 271

fill in the blank 5 = 0.23

fill in the blank 6 = 0.51

Revenue Function (Rev) = PS * (206 - 0.61PS + 0.59PH) + PH * (271 + 0.23PS - 0.51PH)

Taking partial derivatives with respect to PS & PH

d (Rev)/d(PS) = 206 – 1.22PS + 0.59PH +0.23PH

Putting it equal to 0

206 – 1.22PS + 0.82PH =0                 Eq A

d(Rev)/d(PH) = 0.59PS+271+0.23PS-1.02PH

Putting it equal to 0

271+0.82PS-1.02PH=0                                   Eq B

Solving equation A & B

Eq A * 0.82     => 168.9200 – 1.0004PS + 0.6724PH = 0   (C)

Eq B * 1.22     => 330.6200+1.0004PS-1.2444PH = 0           (D)

C+D gives

499.5400 -0.5720PH = 0

=> PH = 873.32

Putting PH = 873.32 I Eq A, we get

PS = 755.84

So, Maximum Revenue

= PS * (206 - 0.61PS + 0.59PH) + PH * (271 + 0.23PS - 0.51PH)

= 755.84 * (206 - 0.61 * 755.84 + 0.59 * 873.32) + 873.32 * (271 + 0.23 * 755.84 - 0.51 * 873.32)

Maximum Revenue = 196,186.52 (Fill in the blank 7)