Chapter 4.6, Problem 66E

Construct a mathematical model for each of the following problems. (The answers in the back of the book include both the mathematical model and the interpretation of its solution.) Use matrix

inverse methods to solve the model and then interpret the solution.

Production scheduling. Labor and material costs for manufacturing two guitar models are given in the table:

(A) If a total of $\$3,000$ a week is allowed for labor and material, how many of each model should be produced each week to use exactly each of the allocations of the $\$3,000$ indicated in the following table?

(B) Is it possible to use an allocation of $\$1,600$ for labor and $\$1,400$ for material? Of $\$2,000$ for labor and $\$1,000$ for material? Explain.