Q2. A printing company Print Tech has designed 4 maps, i.e., A, B, C and D. The map differs in size, colors used, and complexity of the topographical relief. Print Tech has retained a printer to produce the maps. Each map must be printed, cut, and folded. Assume the printer has a limited time in its schedule. The required time in minutes) to perform print, cut and fold for the maps are given as: Map A B D Availability (minutes) Print 1 2 3 3 15000 Cut 2 4 1 3 20000 Fold 3 2 5 3 20000 The profit per map, based on the projected selling price minus printers cost and other variable cost, is equal to $1 for A and B, respectively, and $2 for C and D, respectively. In order to have a sufficiently nice display, at least 1000 unit of each type must be produced. (a) Construct a linear programming model and generate a computer output for the given problem of Print Tech. (5 marks) (b) Utilize the computer output from part (a) to answer the following questions. (1) Determine the production quantities and projected profit. (4 marks) (11) If map B only contributed $0.5 to profit, find the new optimal solution to the problem. (5 marks) (11) Determine the most that Print Tech should be willing to pay for extra printing, cutting, and folding time. (5 marks) [Total : 40 marks]