Chapter 4.6, Problem 64E

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.

Parking receipts. Parking fees at a zoo are $\$5.00$ for local residents and $\$7.50$ for all others. At the end of each day, the total number of vehicles parked that day and the gross receipts for the day are recorded, but the number of vehicles in each category is not. The following table contains the relevant information for a recent 4-day period:

(A) How many vehicles in each category' used the zoo’s parking facilities each day?

(B) If $1,200$ vehicles are parked in one day, is it possible take in gross receipts of $\$5,000$ $5,000? Of $\$10,000$ ? Explain.

(C) Describe all possible gross receipts on a day when $1,200$ vehicles are parked.