11.3 Exercise 71

Construct a system of nonlinear equations to describe the given behavior, then solve for the requested solutions.

A laptop company has discovered their cost and revenue functions for each day: $C \left(x\right) = 3 x^{2} −10 x + 200$ and $R \left(x\right) = −2 x^{2} + 100 x + 50.$ If they want to make a profit, what is the range of laptops per day that they should produce? Round to the nearest number which would generate profit.