A company manufactures two types of sneakers: running shoes and basketball shoes. The total revenue from x1 units of running shoes and y1 units of basketball shoes is: $R = - 3 x _ { 1 } ^ { 2 } - 10 x _ { 2 } ^ { 2 } - 2 x _ { 1 } x _ { 2 } + 50 x _ { 1 } + 96 x _ { 2 }$ , where x1 and x2 are in thousands of units. Find x1 and x2 so as to maximize the revenue.
A) $x _ { 1 } = \frac { 202 } { 29 } , x _ { 2 } = \frac { 119 } { 29 }$
B) $x _ { 1 } = \frac { 119 } { 29 } , x _ { 2 } = \frac { 202 } { 29 }$
C) $x _ { 1 } = \frac { 404 } { 59 } , x _ { 2 } = \frac { 238 } { 59 }$
D) $x _ { 1 } = \frac { 238 } { 59 } , x _ { 2 } = \frac { 404 } { 59 }$
E) $x _ { 1 } = \frac { 119 } { 29 } , x _ { 2 } = \frac { 101 } { 29 }$

Question

Quizplus · Accepted Answer

To maximize the revenue, we need to find the critical points of the revenue function by taking the partial derivatives with respect to $x_1$ and $x_2$, setting them equal to zero, and solving the system of equations. The correct values that maximize the revenue are $x _ { 1 } = \frac { 202 } { 29 }$ and $x _ { 2 } = \frac { 119 } { 29 }$.

A Company Manufactures Two Types of Sneakers: Running Shoes and Basketball