Questions Problem 13-05 (Algorithmic) Question 2 of 6 1. Check My Work 2. eBook
ID: 3365451 • Letter: Q
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Questions Problem 13-05 (Algorithmic) Question 2 of 6 1. Check My Work 2. eBook Problem 13-5 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 = 215-0.6PS 0.25PH DH = 270 0.1PS" 0.55PH The store wishes to determine the selling price that maximizes revenue for these two products. Develop the revenue function for these two models. Choose the correct answer below 4. 6. (i) PsDs PHDHPH(270 0.1Ps 0.55Ph) Ps(215 - 0.6Ps 0.25PH) (ii) PsDs-PHDH = Ps(215-0.6Ps + 0.25PH) -PH(270-0, 1Ps-0.55PH) (iii) PsDs PHDHPs(215 -0.6Ps 0.25PH) + PH(270 + 0.1Ps - 0.55PH) (iv) PsDs-PHDH = Ps(215 + 0.6Ps + 0.25PH) -PH(270-0.1Ps-0.55PH) 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): $ 293 318 Revenue:Explanation / Answer
Ds = 215 - 0.6 Ps + 0.25 PH
DH = 270 + 0.1Ps - 0.55 PH
Maximum Revenue = Ps Ds + PhDh = Ps (215 - 0.6 Ps + 0.25 PH) + Ph (270 + 0.1Ps - 0.55 PH)
so Revenue R = 215 Ps - 0.6 Ps2+ 0.25 PsPH + 270 PH + 0.1 PHPs - 0.55 PH2
so if differentiate revenue with Ps and Ph
dR/dPs = 0 and dR/dPH = 0
dR/dPs = 215 - 1.2 Ps + 0.25 PH + 0.1 PH = 215 - 1.2 Ps + 0.35 PH
dR/dPH = 0.25 Ps + 270 + 0.1 Ps -1.1 PH = 270 + 0.35 Ps -1.1 PH
both these vlaues shall be zero.
215 - 1.2 Ps + 0.35 PH = 0 ..................(i) ;
270 + 0.35 Ps -1.1 PH = 0 ..................(ii)
multiplying equation (i) with 0.35 and second equation (ii) with 1.2
75.25 - 0.42 Ps + 0.1225 PH = 0
324 + 0.42 Ps - 1.32PH = 0
399.25 = 1.1975 PH
PH = 333.403
Ps = (270 -1.1 PH )/0.35 = -(270 - 1.1 * 333.403)/ 0.35 = 276.41
Ps = 276.41
PH = 333.40
Revenue = Ps (215 - 0.6 Ps + 0.25 PH) + Ph (270 + 0.1Ps - 0.55 PH)
Revenue = 276.41 * (215 - 0.6 * 276.41 + 0.25 * 333.40) + 333.40 * (270 + 0.1 * 276.41 - 0.55 * 333.40)
Revenue = $ 74723. 38
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