A clothing manufacturer has 1,000 yd. of cotton to make shirts and pajamas. A shirt requires 1 yd. of fabric, and a pair of pajamas requires 2 yd. of fabric. It takes 2 hr. to make a shirt and 3 hr. to make the pajamas, and there are 1,600 hr. available to make the clothing. a. What are the variables?
b. What are the constraints?
c. Write inequalities for the constraints.
d. Graph the inequalities and shade the solution set.
e. What does the shaded region represent?
f. Suppose he make a profit of $10 on shirts and $18 on pajamas. How would he decide how many of each to make? how many of each should he make assuming he sells all the shirts and pajamas he make?