Question

Jim's Camera shop sells two high-end cameras, the Sky Eagle and Horizon. The demands and selling prices for these two cameras are as follows. Ds = demand for the Sky Eagle Р S = selling price of the Sky Eagle = demand for the Horizon H PH = selling price of the Horizon DHT Ds = 221 – 0.60Ps + 0.35PH = 275 + 0.10Ps - 0.64P, The store wishes to determine the selling price that maximizes revenue for these two products. Develop the revenue function R (in terms of Ps and PH only) for these two models, and find the revenue maximizing prices (in dollars). (Round your answers to two decimal places.) Revenue R = Price for Sky Eagle Ps = $ Price for Horizon Р = $ H R = $ Optimal revenue

Answer 1

Revenue function, R = D_S*P_S + D_H*P_H = (221 - 0.60P_S + 0.35P_H)*P_S + (275 + 0.10P_S - 0.64P_H)*P_H

or, R = 221P_S - 0.60P_S² + 0.35P_HP_S + 275P_H + 0.10P_SP_H - 0.64P_H²

or, R = 221P_S + 0.45P_HP_S + 275P_H - 0.60P_S² - 0.64P_H²

LINGO code:

Max 221 PS 0.60*25*2 + 0.45*PHP5 + 275*PH 0.64*PH^2;

Solution:

PS	304.93
PH	322.05

Optimal revenue = 77976.75