Linear Programming (25 marks) 6. Cranfield Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times in minutes required on each machine for each component are as follows: Component Shaper Grinder 1 3 4 2 2 5 3 2 2 The shaper is available for 120 hours and the grinder is available for 110 hours. No more than 200 units of Component 3 can be sold, but up to 1,000 units of each of the other components can be sold. The company already has orders for 600 units of Component 1 that must be satisfied. The profit contributions of Components 1-3 are 16, 12, and 18 respectively. a. Formulate and solve for the recommended production quantities. [4 marks] b. What are the objective function coefficient ranges for the three components? Interpret these ranges for the company management. [4 marks] C. What are the right-hand-side ranges? Interpret these ranges for company management. [4 marks] d. If more time could be made available on the grinder, how much would it be worth? [4 marks] e. If 500 more units of Component 3 could be sold by reducing the sales price by 4, should the company reduce the price? Explain. [4 marks) f. In a typical product mix model where a company must decide how much of each product to produce, discuss possible situations where there may not be any feasible solution. Could this be realistic? If you had such a situation in your company, how might you proceed? (5 marks]