Question

Jim's Camera shop sells two high-end cameras, the Sky Eagle and Horizon. The demand for these two cameras are as follows (DS = demand for the Sky Eagle, Ps is the selling price of the Sky Eagle, DH is the demand for the Horizon and PH is the selling price of the Horizon):

Ds = 230 - 0.5PS + 0.38PH

DH = 260 + 0.1Ps - 0.62PH

Find the prices that maximize revenue.

If required, round your answers to two decimal places.

Optimal Solution:

-Selling price of the Sky Eagle (Ps):_______

-Selling price of the Horizon (PH):_______

-Revenue:_______

Answer 1

According to the given question, Jim's Camera shop sells two high-end cameras, the Sky Eagle and Horizon. The demand for these two cameras are as follows (DS = demand for the Sky Eagle, Ps is the selling price of the Sky Eagle, DH is the demand for the Horizon and PH is the selling price of the Horizon), where the demand function is written as:

the demand for the Sky Eagle:

and the demand for the Horizon:

Therefore the revenue function is determined as:

  

To find out the maximum value of revenue we take partial derivative with respect to   as

:

by solving equation (i) and (ii)x2.0833 we get:

  

......................................................................

from equation (i) we get

and therefore total revenue is determined as:

Therefore  Optimal Solution:

-Selling price of the Sky Eagle (Ps):

-Selling price of the Horizon (PH):

Revenue: