2. Small and Short is ordering suits for its spring season. It orders four styles of suits: (1) polyester blend suits, (2) pure wool suits, (3) pure cotton suits, and (4) imported fine suits. The following table gives the unit profit per suit as well as the estimates for per unit salesperson hours, advertising dollars, and floor space required. Unit Salesperson Advertising Suit Profit Hours Dollars Polyester $35 0.4 $2 Wool $47 0.5 $4 Cotton $30 0.3 $3 Import $90 1.0 $9 Display Space (ft) 1.00 1.50 1.25 3.00 The spring season will last 90 days. Small and Short is open an average of 10 hours a day, 7 days a week; an average of two salespersons should be in the suit department when the store is open. 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 a linear program to determine the number of each type of suit to pur- chase for the spring season so as to maximize profit. (6) Convert the linear program to equation standard form and solve the resulting model using Matlab (or other software). (c) The variables that are positive in the optimal solution are the optimal basic vari- ables. Using this information, construct a final simplex tableau for this problem. (d) Formulate the dual for the model you created part (a) of the previous problem. (e) Provide an economic interpretation of the dual LP. (f) Use complementary slackness to solve the dual LP. (9) How do the optimal dual values relate to the shadow prices of the functional con- straints of the primal problem? 2. Small and Short is ordering suits for its spring season. It orders four styles of suits: (1) polyester blend suits, (2) pure wool suits, (3) pure cotton suits, and (4) imported fine suits. The following table gives the unit profit per suit as well as the estimates for per unit salesperson hours, advertising dollars, and floor space required. Unit Salesperson Advertising Suit Profit Hours Dollars Polyester $35 0.4 $2 Wool $47 0.5 $4 Cotton $30 0.3 $3 Import $90 1.0 $9 Display Space (ft) 1.00 1.50 1.25 3.00 The spring season will last 90 days. Small and Short is open an average of 10 hours a day, 7 days a week; an average of two salespersons should be in the suit department when the store is open. 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 a linear program to determine the number of each type of suit to pur- chase for the spring season so as to maximize profit. (6) Convert the linear program to equation standard form and solve the resulting model using Matlab (or other software). (c) The variables that are positive in the optimal solution are the optimal basic vari- ables. Using this information, construct a final simplex tableau for this problem. (d) Formulate the dual for the model you created part (a) of the previous problem. (e) Provide an economic interpretation of the dual LP. (f) Use complementary slackness to solve the dual LP. (9) How do the optimal dual values relate to the shadow prices of the functional con- straints of the primal