Question

U.S. Labs manufactures mechanical heart valves from the heart valves of pigs. Different heart operations require valves of different sizes. U.S. Labs purchases pig valves from three different suppliers. The cost and size mix of the valves purchased from each supplier is given in Table 3. Each month, U.S. Labs places one 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 700 valves per month can be purchased from each supplier. Formulate an LP that can be used to minimize the cost of acquiring the needed valves

Answer 1

To minimize the cost of acquiring the needed heart valves, U.S. Labs can formulate a linear programming (LP) model with appropriate constraints and an objective to minimize the total cost. This model can be solved using software to determine the optimal number of valves to purchase from each supplier.

Step-by-step explanation:

To minimize the cost of acquiring the needed valves, U.S. Labs can formulate a linear programming (LP) model. Let's define the decision variables as x1, x2, and x3 representing the number of valves purchased from each of the three suppliers, respectively. The objective is to minimize the total cost, which can be expressed as the sum of the product of the cost per valve and the number of valves purchased from each supplier.

The constraints include:

1. The minimum number of large valves required: x1 + x2 + x3 ≥ 500
2. The minimum number of medium valves required: x1 + x2 + x3 ≥ 300
3. The minimum number of small valves required: x1 + x2 + x3 ≥ 300
4. The maximum number of valves that can be purchased from each supplier: x1 ≤ 700, x2 ≤ 700, x3 ≤ 700

This LP model can be solved using appropriate software to determine the optimal number of valves to purchase from each supplier to minimize costs.