Question

A company's weekly profit can be modeled by the equation y=-0.5x^2+50x-300 where y is the profit (in dollars) and x is the number of items sold. What is their maximum weekly profit ?

Answer 1

Explanation:

The number of items sold that gives the max profit is found in the vertex of this quadratic, (h, k). Lucky for us we have a formula for k that will give us exactly what we are looking for, and nothing else.

`k=c-(b^2)/(4a)` where a = -.5, b = 50, and c = -300:

`k=-300-(50^2)/(4(-.5))=-300+1250=950`

The max profit is $950 per week