a company manufactures and sells widgets. the revenue (in dollars) generated by selling x widgets per week…

a company manufactures and sells widgets. the revenue (in dollars) generated by selling x widgets per week is given by the quadratic equation ( r = - 2 x ^ { 2 } + 100 x ).\na) what is the maximum revenue the company can generate per week?\nb) how many widgets must the company sell per week to maximize revenue?

a company manufactures and sells widgets. the revenue (in dollars) generated by selling x widgets per week is given by the quadratic equation ( r = - 2 x ^ { 2 } + 100 x ).\na) what is the maximum revenue the company can generate per week?\nb) how many widgets must the company sell per week to maximize revenue?

Answer

Explanation:

Step1: Find the vertex of the quadratic function

For a quadratic function (y = ax^{2}+bx + c), the (x) - coordinate of the vertex is given by (x=-\frac{b}{2a}). In the revenue function (R=-2x^{2}+100x), (a=-2) and (b = 100). [x=-\frac{100}{2\times(-2)}=\frac{-100}{-4} = 25]

Step2: Calculate the maximum revenue

Substitute (x = 25) into the revenue function (R=-2x^{2}+100x). [R=-2\times(25)^{2}+100\times25=-2\times625 + 2500=-1250+2500 = 1250]

Answer:

a) (1250) dollars b) (25) widgets