The maximum number of labor hours available per day at Shirts Happen are 25 hours

Directions: Please read and complete the following on a separate sheet of paper.
Clearly explain your answers, using your own words.
“Shirts Happen”: An application in resource allocation and linear programming
The Shirts Happen Clothing Company manufactures men’s shirts and women’s blouses. The
production process includes cutting, sewing, and packaging. The table below gives the labor requirements (in minutes) for each type of garment:
Minutes per garment
Cutting Sewing Packaging
Men’s shirts 30 80 12
Women’s blouses 60 60 4
The maximum number of labor hours available per day at Shirts Happen are 25 hours for
cutting, 35 hours for sewing, and 5 hours for packaging.
1. Let x represent the number of men’s shirts produced per day by the Shirts Happen Clothing
Company, and let y represent the number of women’s blouses produced per day. Write a
system of five linear inequalities involving x and y that, when solved, give the set of all
ordered pairs (x, y) of number of men’s shirts and number of women’s blouses that Shirts
Happen can produce per day, given the constraints above. Next to each inequality, write a
brief description or interpretation of its meaning.
2. Carefully graph the system of linear inequalities on a separate sheet of graph paper and then
shade the feasible region. Is it bounded or unbounded? Identify and label on your graph the
coordinates of each of the corner points. Attach the graph along with your work.
3. For each of the following solutions, determine whether or not it is a feasible solution to the
Shirts Happen Clothing Company problem. Show your work and explain your reasoning.
(a). 5 men’s shirts per day, 20 women’s blouses per day
(b). 25 men’s shirts per day, 25 women’s blouses per day
(c). 0 men’s shirts per day, 0 women’s blouses per day
(d). –10 men’s shirts per day, –20 women’s blouses per day
(e). 10 men’s shirts per day, 10 women’s blouses per day
(f). 18 men’s shirts per day, 14 women’s blouses per day
4. Suppose that each men’s shirt produced and sold yields a $25 profit and each women’s blouse
produced and sold yields a $50 profit.
(a). An isoprofit line is a line of solution points (x, y) within the feasible region that each
yield the same profit. Find two feasible solutions to the Shirts Happen Clothing Company
problem that produce a total profit of $200, and then find two feasible solutions that produce
a total profit of $500. Explain your answers, and then draw these two isoprofit lines on your
graph — one for a total profit of $200, and the other for a total profit of $500.
(b). Finding optimal solution(s): How many men’s shirts and women’s blouses should the
Shirts Happen Clothing Company produce each day so as to maximize its daily profit? What
is the company’s maximum daily profit as a result? Hint: There are actually multiple optimal
solutions. List and explain two of them. Would there be a reason for the Shirts Happen
Clothing Company to favor one optimal solution over another? Clearly explain your reasoning
along with any additional assumptions that need to be made in determining an optimal
solution to this problem.