6. An engineering firm specialises in converting standard trucks and vans in caravanettes. The conversion takes place in two workshops, the assembly shop where the structural alterations occur, and the finishing shop where the vehicles are fitted out. At present, the firm has a weekly capacity of 180 man-days in assembly shop and 135 man-days in finishing shop. Each truck requires 5 man- days to assemble, but each van only requires 2 man-days. Both vehicles require 3 man-days in the finishing shop. Each converted van earns 40 profit and each converted truck earns 200 profit. The firm has a contract to supply 10 converted trucks per week for export. Find the output combination that would maximise profit. (20 Marks) 7. Find any maximum and minimum turning points of y = 12x x3 and between them. (5 Marks) distinguish 8. A firm is producing two brass ornaments, a standard and a deluxe. The manufacturing process consists of two machines only: Standard Model Deluxe Model Machine 1 1 Hour 2 Hours Machine 2 1 Hour 5 Hours There are 20 hours available on machine 1 and 35 hours on machine 2. The firm makes a profit of 0.50 on the standard model and 1.50 on a deluxe model. Determine the output that would maximise profit. (10 Marks) 9. Sketch the solution set for the triple inequalities: x + y 2 2 x + 4y = 4 y>-1