7. The Gutchi Company manufactures purses, shaving bags, and backpacks. The construction of the three products requires leather and synthetics, with leather being the limiting raw material. The production process uses two types of skilled labor: sewing and finishing. The following table gives the availability of the resources, their usage by the three prod- ucts, and the prices per unit. Resource requirements per unit Resource Purse Bag Backpack Leather (ft²) 2 3 Sewing (hr) 2 1 Finishing (hr) 5 Price ($) 24 22 55 45 Daily availability 435 42 40 Formulate the problem as a linear program, and find the optimum solution. Next, indicate whether the following changes in the resources will keep the current solution feasible. For the cases where feasibility is maintained, determine the new optimum solution (values of the variables and the objective function). (a) Available leather is increased to 45 ft2. (b) Available leather is decreased by 1 ft². (c) Available sewing hours are changed to 38 hrs. (d) Available sewing hours are changed to 46 hrs. (e) Available finishing hours are decreased to 15 hrs. (f) Available finishing hours are increased to 50 hrs. (g) Would you recommend hiring an additional sewing worker at $15 an hour?