Nice Shoes Inc manufactures and sells two different types of shoes: boots and sneakers. A pair of boots costs $22 to produce and sells for $32, while a pair of sneakers costs $18 to produce and sells for $26. The labor requirements for a pair of boots are: 2 hours to make the shoelaces, 4 hours to make the shoe upper & sole, 2 hours to sew, and 1 hour to package. The labor requirements for a pair of sneakers are: 1 hour to make the shoelaces, 5 hours to make the shoe upper & sole, 3 hours to sew, and 1 hour to package. The Nice Shoes Inc employees have different jobs in the production of shoes. Today, 21 employees showed up to make shoelaces, 60 to make the shoe uppers & soles, 40 to sew the shoes together, and 20 to package the shoes. All employees at Nice Shoes Inc work a 10-hour workday. Assuming that all shoes produced can be sold, what is the optimal production mix of boots and sneakers that would maximize the day's profits? 

 

a) Write out the LP model for this problem (the equation to optimize and all constraints). 

 

b) Determine the optimal solution either by using level curves or modeling with Solver. Show your work for whichever method you use and provide a brief interpretation of your results, including what the profits would be for the day. 

 

c) If three more shoelace makers had shown up for the day, would it have changed your optimal production mix and profits? Why or why not?