Chapter 4.6, Problem 63E

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.

Concert tickets. A concert hall has $10,000$ scats and two categories of ticket prices, $\$25$ and $\$35.$ Assume that all seats in each category can be sold.

(A) How many tickets of each category should be sold to bring in each of the returns indicated in the table?

(B) Is it possible to bring in a return of $\$200,000$ ? Of $\$400,000$ ? Explain.

(C) Describe all the possible returns.