Objective Function Maximize =

Subject to:

Packaging Material

Subject to

Packing Time

Leach Distributors packages and distributes industrial supplies. A standard shipment can be packaged in a class A container, a class K container, or a class T container. A single class A container yields a profit of $10; a class K container, a profit of $8; and a class T container, a profit of $12. Each shipment prepared requires a certain amount of packing material and a certain amount of time. Formulate and solve this problem using LP software. Decision variables: X1 = number of class A containers to be used X2 = number of class K containers to be used X3 = number of class T containers to be used Resources Needed per Standard Shipment Class of Container K T Total amount of resource available per week Packing Material (pounds) 2 1 3 Packing Time (hours) 2 6 4 120 pounds 210 hours Hugh Leach, head of the firm, must decide the optimal number of each class of container to pack each week. He is bound by the previously mentioned resource restrictions but also decides that he must keep his 6 full-time packers employed all 210 hours (6 workers x 35 hours) each week. Objective function: Maximize Z= Subject to: (packing material) (packing time) X1, X2, X3 20 $10 X1 + $8 X2 + $12 X3 120 X1 + 210 X2 X1 + X2 + X3 2 X1 + 1 X2 + 3 X3 s 120 2 X1 + 1 X2 +3 X3 2 120 X1 + X2 + X3 120 2 X1 + 6 X2 +4 X3 = 210 X1 + X2 + X3 s 210 2 X1 +6 X2 + 4 X3 2 210