Question

The daily profit P for a cake bakery can be modeled by the function P(x)= -15x^2 +330x -815. What should the price of a cake be to provide a daily profit of at least $600? Round answers to the nearest dollar.

Answer 1

`5\leq \: x\leq 16`

Explanation:

The daily profit P for a cake bakery is modeled by the function

`P(x)= -15x^2 +330x -815.` where x=Price of Cakes Sold

We want to determine the value of x which will provide a daily profit of at least $600.

`-15x^2 +330x -815\leq 600`

`-15x^2 +330x -815-600\leq 0\\ -15x^2 +330x-1415\leq 0\\\text{Using Calculator to solve the quadratic equation}\\5.83\leq x \: or \: x\leq 16.16\\5\leq x\leq 16`

The minimum Price which the cakes can be sold is represented by the inequality

`5\leq \: x\leq 16`