Min and max The daily profit dollars of a company making tab

Min and max

The daily profit dollars of a company making tables is described by the function p(x)= - 5x^2 + 240x - 2635,where x is the number tables that manufactured in 1 day. The maximum profit of the company occurs at the vertex of the parabola. How many tables should be made per day in order to obtain the maximum profit for the company? what is the maximum profit? To obtain the maximum profit for the company.

Solution

we know the equation of parabola in vertex form is y=a(x-h)^2+k

writing the given equation in that form we get

y=-5(x-24)^2+245

so the vertex is 24,245

as maximum profit occurs at vertex, the number tables per day is 24.

Maximum profit is=245