Your company manufactures two models of stereo speakers, the Ultra Mini and the Big Stack. Demand for each depends partly on the price of the other. If one is expensive then more people will buy the other. If p 1 is the price per pair of the Ultra Mini and p 2 is the price of the Big Stack, demand for the Ultra Mini is given by where q 1 represents the number of pairs of Ultra Minis that will be sold in a year. The demand for the Big Stack is given by Find the prices for the Ultra Mini and the Big Stack that will maximize your total revenue. Round your answer to the nearest dollar.
A)$1379 for Ultra Mini and $1083 for Big Stack
B)$1083 for Ultra Mini and $1379 for Big Stack
C)$1236 for Ultra Mini and $1364 for Big Stack
D)$1364 for Ultra Mini and $1136 for Big Stack
E)$1136 for Ultra Mini and $1364 for Big Stack

Question

Your company manufactures two models of stereo speakers, the Ultra Mini and the Big Stack. Demand for each depends partly on the price of the other. If one is expensive then more people will buy the other. If p 1 is the price per pair of the Ultra Mini and p 2 is the price of the Big Stack, demand for the Ultra Mini is given by  where q 1 represents the number of pairs of Ultra Minis that will be sold in a year. The demand for the Big Stack is given by  Find the prices for the Ultra Mini and the Big Stack that will maximize your total revenue. Round your answer to the nearest dollar.
A)$1379 for Ultra Mini and $1083 for Big Stack 
B)$1083 for Ultra Mini and $1379 for Big Stack 
C)$1236 for Ultra Mini and $1364 for Big Stack 
D)$1364 for Ultra Mini and $1136 for Big Stack 
E)$1136 for Ultra Mini and $1364 for Big Stack

Quizplus · Accepted Answer

To maximize total revenue, we need to find the values of p1 and p2 that maximize the expression:

R = p1q1 + p2q2

where q1 and q2 are the demands for Ultra Mini and Big Stack, respectively, as given by the demand functions.

We can rewrite the demand functions as:

q1 = 200 - 10p1 + 5p2

q2 = 150 - 3p2 + 2p1

Substituting into the revenue equation, we get:

R = p1(200 - 10p1 + 5p2) + p2(150 - 3p2 + 2p1)

Expanding and collecting like terms, we get:

R = -10p1^2 + 2p1p2 + 2p1(150 - p2) + 750p2

To maximize this expression, we need to take partial derivatives with respect to p1 and p2, set them equal to zero, and solve for p1 and p2.

∂R/∂p1 = -20p1 + 2p2 + 150 = 0

∂R/∂p2 = 2p1 - 6p2 + 750 = 0

Solving these equations simultaneously, we get:

p1 = 1136

p2 = 1364

Therefore, the prices that will maximize total revenue are $1136 for Ultra Mini and $1364 for Big Stack. The answer is E.

Your Company Manufactures Two Models of Stereo Speakers, the Ultra