A company that produces portable cassette players estimates that the profit P (in dollars) for selling a particular model is P=-76x^3+4830x^2-320000, 0 is less than or equal to x is less than or equal to 50, where x is the ad expense (in tens of thousands of dollars). using this model, find the smaller of two ad amounts that will yield profit of $800000.

Question

A company that produces portable cassette players estimates that the profit P (in dollars) for selling a particular model is P=-76x^3+4830x^2-320000, 0 is less than or equal to x is less than or equal to 50, where x is the ad expense (in tens of thousands of dollars). using this model, find the smaller of two ad amounts that will yield profit of $800000.

Answer 1

you must have a method of solving

800000 = -76x^3 + 4830x^2 - 320000

Wolfram yields two answers,
one of appr 18 , the other appr 59.3

http://www.wolframalpha.com/input/?i=solve+800000+%3D+-76x%5E3+%2B+4830x%5E2+-+320000

Answer 2

To find the smaller of two ad amounts that will yield a profit of $800,000, we need to solve the equation P = 800,000 for x.

Given the profit model P = -76x^3 + 4830x^2 - 320,000, we can substitute P = 800,000 into the equation and solve for x.

800,000 = -76x^3 + 4830x^2 - 320,000

To make the equation easier to work with, we can rearrange it as follows:

-76x^3 + 4830x^2 - 320,000 - 800,000 = 0

Simplifying the equation further:

-76x^3 + 4830x^2 - 1,120,000 = 0

Now, we can use a numerical method or graphing calculator to find the values of x that satisfy this equation. In this case, since the bounds are given as 0 ≤ x ≤ 50, we can use the graphical method.

Plotting the equation -76x^3 + 4830x^2 - 1,120,000 = 0 on a graphing calculator or graphing software, we can find two values of x for which the equation is satisfied. The smaller of these values will be the answer to the problem.