Question

A rice store estimates that if it sells each pack of rice forxdollars, then the projected number of packssold daily is 240−10x. What is the price per pack that maximizes its daily profit?

Answer 1

Price per pack = 12

Explanation:

The profit can be calculated as the product of the price by the quantity sold:

P = x * (240-10x)

P = -10x^2 + 240x

To find the maximum of this quadratic function, we can use the formula to find the vertix:

x_v = -b/2a

Where a and b are coefficients of the quadratic equation (a = -10 and b = 240)

x_v = -240/(-20) = 12

Now, we use this value to find the maximum profit:

P_max = -10*(12)^2 + 240*12 = 1440