Revenue, cost, and profit functions. A company manufactures 10- and 3-speed bicy

Question

Revenue, cost, and profit functions. A company manufactures 10- and 3-speed bicycles. The weekly demand and cost equations are p = 230 minus 9x + y q = 130 + x minus 4y C(x, y) = 200 + 80x + 30y where $p is the price of a 10-speed bicycle, $q is the price of a 3-speed bicycle, x is the weekly demand for 10-speed bicycles, y is the weekly demand for 3-speed bicycles, and C(x, y) is the cost function. Find the weekly revenue function R(x, y) and the weekly profit function P(x, y).Evaluate R(10, 15) and P(10, 15).

Explanation / Answer

q = price of a 3-speed bicycle
p = price of a 10-speed bicycle
x = weekly demand for 10-speed bicycles
y = weekly demand for 3-speed bicycles
p = 230 - 9x + y
q = 130 + x - 4y
C(x,y) = 200 + 80x +30y
C(10,15) = 200 + 80(10) +30(15) = 1450
R(x,y) = px + qy
R(x,y) = (230 - 9x + y)x + (130 + x - 4y)y
R(10,15) = 2750
P(x,y) = R(x,y) - C(x,y)
P(10,15) = R(10,15) - C(10,15) = 2750 - 1450 = 1300

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