Question

Please answer each question and highlight the answers. Please show work. Please round over two decimal places.

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-230-0.5 Ps + 0.38 PH DH-260+0.1 Ps-0.62 PH The store wishes to determine he selling price hat maximizes revenue or hese two products. Se ect he revenue unction or ese ю model Choose e correct answer lo (i) P, D, + PhDH-Pn(260-0.1 P.-0.62 P.) + Ps(230-0.5 Pe+ 0.38 Ph) (İİ) Ps Ds . PH DH-PS(230-0.5 P, + 0.38 PH)-PH(260 . 0.1 Ps . О.62 PA) Cii)Ps Ds+PH DH-P (230-0.5 P0.38 PH)P(2600.1 P 0.62 P) (iv) Ps Ds-PH DH- Ps(230+0.5 Ps +0.38 PH)-PH(260- 0.1 Ps -0.62 PH) Option (iii) 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

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 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) " 215-0.5Ps + 0.15% -260+ 0.2Ps 0.45P store wishes to determine the selling price that maximizes revenue for these two products. Develop the revenue function for these two models. C correct answer below. Ans.: The revenue function is given by, But D, = 215-05P +0.15P D 26002P-0.45P Thus, R(R,%)-P(215-05P +0.15%)+Po(260+0.2 -0.45%) - 215P-0.5p +0.15PP, +260 P, +0.2PP-0.45P* -21 5P-05P2 +0.35P昂+ 260P -0.45P Find the prices that maximize revenue. If required, round your answers to two decimal places. Ans.: By taking the partial derivatives of R(P, P)215P -0.5P +0.35P.P +260P-0.45P, and equating to zero, this gives R(2,昂)-215P-0.5P. +0.35ZZ +260 -0.45玲 CR -215-P +0.35 -0 P-0.35P 215 OR aP -0.35P = 260 0.35P 260-0.90P. 0 0.90

0by 3d adnto003,s gives, 0.35(2-0.35%)= 0.35x 215 0.35P-0.1225昂ー7525 0.90P-0.35P-260 , 0.35P-0.1225P + 0.90P-0.35P-7525+ 260 0.7775P 335.25 p 33525 0.7775 $431.19 215, this gives Substitute P $431.19 into R-035P P-0.35x43 1.19-215 = 215+0.35x431.19= $365.92 Thus P $431.19 P $365.92 Substitute P $431.19, P $365.92 into R(PRo)-219,-05P2 +0.35ZZ +260P -0.4%, this gives, R(P.P)-215x36592-0.5x(365.92)+035 x365.92x431.19 260x431.19-0.45x(431.19) - $95,390.68