Jim\'s Camera shop sells two high-end cameras, the Sky Eagle and Horizon. The de
ID: 2949406 • Letter: J
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:_______
Explanation / Answer
Answers:
Selling price of the Sky Eagle (Ps): 396.26
Selling price of the Horizon (PH): 363.02
Revenue: 176062.5
Solution:
given,
demand for sky eagle camera Ds = 230 - 0.5PS + 0.38PH
demand for horizon camera DH = 260 + 0.1Ps - 0.62PH
// revenue = demand times price
since we have 2 products revenue = Ds * Ps + DH * PH
revenue = Ps(230 - 0.5PS + 0.38PH) + PH(260 + 0.1Ps - 0.62PH)
= 230Ps - 0.5(Ps)^2 + 0.38PH.Ps + 260PH + 0.1Ps.PH - 0.62(PH)^2
simplifing the equation by derivating twice (once with respective to Ps and again with respective to PH)
dR / dPs = 230 - 1(Ps) + 0.358PH + 0 + 0.1PH - 0
= 230 - 1(Ps) + 0.458PH ....................let this be equation 1
dR / dPH = 0 - 0 + 0.38 Ps + 260 + 0.1Ps - 1.24 PH
= 260 + 0.48 Ps - 1.24 PH .........................let this be equation 2
solve equation 1 and 2 to get the unknown variables
1 x equation (1) = 230 - 1(Ps) + 0.458PH
2.084 x equation (2) = 541.84 +1(Ps) - 2.58416PH
by adding we get,
= 771.84 - 2.12616 PH = 0 // dR/ dPs = dR/ dPH = 0
= PH = 771.84/2.12616 = 363.0207
substituting PH in one of the equations to get Ps
= 230 - 1(Ps) + 0.458(363.0207) = 0
= 230 - Ps = - 166.2634806
= - Ps = - 166.2634806 - 230
= Ps = 396.2634
Revenue = 230Ps - 0.5(Ps)^2 + 0.38PH.Ps + 260PH + 0.1Ps.PH - 0.62(PH)^2
= 176062.5
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.