Problema Solution
Suppose the profit function for a company selling x items of a product is given by f(x)=-6x^2+720x-12500.
a. what number of units will maximize the companys profit for this product?
b. what is the maximum profit?
Answer provided by our tutors
We need to find the maximum of the quadratic function f(x)=-6x^2+720x-12500 and the value of x for which it is achieved.
f max = c - (b^2)/(4a)
x max = -b/(2a)
where a = -6, b = 720, c = -12500
f max = -12500 - (720^2)/(4*(-6))
f max = $9,100
x max = -720/(2*(-6))
x max = 6o units
a. The number of units that will maximize the company's profit is 60.
b. The maximum profit is $9,100.
We can also see the solution if we graph the function: y = -6x^2+720x-12500
The vertex gives the solution.