RETAILING. Bullox Department Store is ordering suits for its spring season. It orders four styles of suits. Three are “off-the-rack suits”: (1) polyester blend suits, (2) pure wool suits, and (3) pure cotton suits. The fourth style is an imported line of fine suits of various fabrics. Studies have given Bullox a good estimate of the amount of hours required of its sales staff to sell each suit. In addition, the suits require differing amounts of advertising dollars and floor space during the season. The following table gives the unit profit per suit as well as the estimates for salesperson-hours, advertising dollars, and floor space required for their sale.
Bullox expects its spring season to last 90 days. The store is open an average of 10 hours a day, 7 days a week; an average of two salespersons will be in the suit department. The floor space allocated to the suit department is a rectangular area of 300 feet by 60 feet. The total advertising budget for the suits is $15,000.
a. Formulate the problem to determine how many of each type of suit to purchase for the season in order to maximize profits and solve as a linear program
b. For polyester suits, what would be the effect on the optimal solution of i. overestimating their unit profit by $1 ; by $2 ? ii. underestimating their unit profit by $1 ; by $2 ?
c. Show whether each of the following strategies, individually, would be profitable for Bullox:
i. utilizing 400 adjacent square feet of space that had been used by women’s sportswear. This space has been projected to net Bullox only $750 over the next 90 days.
ii. spending an additional $400 on advertising.
iii. hiring an additional salesperson for the 26 total Saturdays and Sundays of the season. This will cost Bullox $3600 in salaries, commissions, and benefits but will add 260 salesperson-hours to the suit department for the 90-day season.
d. Suppose we added a constraint restricting the total number of suits purchased to no more than 5000 for the season. How would the optimal solution be affected?