A company produces two types of doghouses, regular and deluxe. A regular doghouse requires 7 hours to build and 3 hours to paint. A deluxe doghouse requires 11 hours to build and 4 hours to paint. The company employs 5 builders and 2 painters. Each employee can work a maximum of 40 hours.
a. Write a system of inequalities that can be used to find the number of each type of doghouse built in a week. Define the variables you use in your system.