A company manufactures mechanical heart valves from the heart valves of pigs. Different heart operations require valves of different sizes. The company purchases pig valves from three different suppliers. The cost and size mix of the valves purchased from each supplier are given in the following table.

	Cost/valve	% small	% medium	% large
Supplier 1	$20	40	40	20
Supplier 2	$16	30	35	35
Supplier 3	$12	20	20	60

Each month, the company places an order with each supplier. At least 500 large, 300 medium and 300 small valves must be purchased each month. Because of the limited availability of pig valves, at most 500 valves per month can be purchased from each supplier.

1. Provide the complete linear programing formulation. Clearly specify decision variables, objective function and constraints.
2. Build a model in Excel and paste a screenshot here. Use FORMULATEXT in your model to show calculations.
3. Use Solver to determine how the company can minimize the cost of acquiring the needed valves. What is the optimal order plan? What is the minimum total cost?
4. Use SolverTable to investigate the effect on total cost of increasing its minimal purchase requirements each month. Specifically, see how the total cost changes as the minimal purchase requirements of large, medium, and small valves all increase from their original values by the same percentage. Revise your model so that SolverTable can be used to investigate these changes when the percentage increase varies from 2% to 20% in increments of 2%.