As marketing director for a bicycle manufacturer, you come up with the following
ID: 2839169 • Letter: A
Question
As marketing director for a bicycle manufacturer, you come up with the following scheme: You will offer to sell a dealer x bicycles and y tricycles for R(x, y) = 3,700 - 3,700e^0.02x-0.01y dollars. Find a formula for your marginal revenue for bicycles: At a sales level of x bicycles and y tricycles, additional bicycles will sell for approximately Rx = dollars per bicycle. Find a formula for your marginal revenue for tricycles: At a sales level of x bicycles and y tricycles, additional tricycles will sell for approximately Ry = dollars per tricycle. If a dealer purchases loo bicycles and 200 tricycles, approximately how much would that dealer pay for an additional bicycle? dollars. (Round to 2 decimal places.)Explanation / Answer
Total revenue formula (R) = 3700 - 3700e-0.02x - 0.01y
Now, marginal revenue w.r.t. bicycles
= partial derivative w.r.t x
= 0 - 3700(-0.02) e-0.02x - 0.01y
= 74e-0.02x - 0.01y
Similarly, marginal revenue w.r.t tricycles = partial derivative w.r.t y
= 0 - 3700 (-0.01) e-0.02x - 0.01y
= 37 e-0.02x - 0.01y
Now, Given that we have 100 bicycles and 200 tricycles,
Rx = 74e-0.02(100) - 0.01(200)
= 74 e-4
= 1.355 $
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