The American Edwards Laboratories

(AEL)10 manufactures artificial human heart valves from pig hearts. One of the things making planning complex is that the size of pig hearts is highly variable, depending on breed, age when slaughtered, feed mix, and so on. The following

(fictitious) table shows the fraction of hearts from suppliers j = 1,c, 5 yielding each of the valve sizes i = 1,c, 7, along with the maximum quantity available from each supplier per week and the unit cost of hearts obtained.

Supplier j Size 1 2 3 4 5 1 0.4 0.1 — — —

2 0.4 0.2 — — —

3 0.2 0.3 0.4 0.2 —

4 — 0.2 0.3 0.2 —

5 — 0.2 0.3 0.2 0.2 6 — — — 0.2 0.3 7 — — — 0.2 0.5 Availability 500 330 150 650 300 Cost 2.5 3.2 3.0 2.1 3.9 AEL wants to decide how to purchase hearts to meet weekly requirements of 20 size 1, 30 size 2, 120 size 3, 200 size 4, 150 size 5, 60 size 6, and 45 size 7 valves at minimum total cost.

(a) Formulate an LP model of this heart purchase planning problem using the decision variable (j = 1,c, 5)

xj ! number of hearts purchased weekly from supplier j

(b) Enter and solve your model with the class optimization software.