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Question 1050626: i am having trouble with theese 2
1: y = g(x) = -2x^2 - 6x
2: The demand function for an electronics company's laptop computer line is p = 2400 - 6q , where p is the price (in dollars) per unit when q units are demanded (per week. Find the level of production that maximizes the manufacturer's total revenue and determine this revenue.
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website! 1. g(x) = -2x^2 - 6x
Completing Square:
g(x) = -2(x^2 - 3x)
g(x) = -2(x^2 - 3x + (3/2)^2) + 2(3/2)^2
g(x) = -2(x - 3/2)^2 + 9/2
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Revenue functions R(x) = px where p is a function of x (price p at x produced, for ex.)
2.
p = 2400 - 6q
R(q) = (2400-6q)q
R(q) = -6q^2)+ 2400q
Completing Square:
R(q) = -6(q^2 - 400q)
R(q) = -6(q^2 - 400q + 200^2)+ 6(200^2)
R(q) = -6(q - 200)^2 + 6(200^2) Parabola Opening Downward V(200, 240,000)
q = 200 maximizes Revenue = $240,000
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