The Salt Creek Soap Company has determined the following nonlinear model to determine the optimal pounds of industrial soap (X1) and shampoo (X2) it should produce each day.
Maximize Z = X1² + 2X2² - 8X1 - 12X₂ + 34
Subject to: X₁ + 2X₂ = 4 lbs
-What is profit when the optimal values of soap and shampoo are produced?

Question

Quizplus · Accepted Answer

Given the constraint X1 + 2X2 = 4, we can solve for one variable in terms of the other (e.g., X1 = 4 - 2X2) and substitute it into the objective function Z = X1^2 + 2X2^2 - 8X1 - 12X2 + 34. After solving the resulting equation for its maximum value, we find that the profit, Z, when the optimal values of soap and shampoo are produced, is 14.

The Salt Creek Soap Company Has Determined the Following Nonlinear