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1) Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components.

Supplier
Component123
1$12$13$14
2$10$11$10
Each supplier has a limited capacity in terms of the total number components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two compoents, if the total number of units ordered is within its capacity. Supplier123

Capacity6001000800
If the Edwards production plan for the next period includes 1000 units of component 1 and 800 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier? What is the total purchase cost for the components?

2) Two types of crude oil are used to produce two grades of gasoline. The percentage of important ingredients (A and B) in each type of crude oil differs as does the cost per gallon as shown below:

Crude oil Cost/gallon Ingredient A Ingredient B
1 $0.10 20% 60%
2 $0.15 50% 30%
Each gallon of regular gasoline must contain at least 40% of A, whereas each gallon of high octane can contain at most 50% of B. Daily demand for regular octane gasoline is 800,000 gallons and daily demand for high octane is 500,000 gallons. How many gallons of each type of crude oil should be used in regular and in high octane gasoline in order to satisfy the daily demand at a minimum cost?

3) Frandec Company manufactures, assembles, and rebuilds material hand equipment used in warehouses and distribution centers. One product, called a Liftmaster is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec is planning a production of 5000 Liftmasters next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may either be manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown.

|Component |Manufacturing Costs |Purchase cost | |Frame |$38.00 |$51.00 | |Support |11.50 |15.00 | |Strap |6.50 |7.50 |

Three departments are involved in the production of these components. The time (in min per unit) required to process each component in each department is given, along with available capacity (in hours) for the three departments. |Component |Cutting Dept |Milling Dept |Shaping Dept | |Frame |3.5 |2.2 |3.1 | |Support |1.3 |1.7 |2.6 | |Strap |0.8 |- |1.7 | |Capacity |350 |420 |680 |

a. Formulate and solve a linear programming model for this make-or-buy application. How many of each component should be manufactured and how many should be purchased? b. What is the total cost of the manufacturing and purchasing plan? c. How many hours of production time are used in each department? d. How much should Frandec be willing to pay for an additional hour of time in the shaping department? e. Another manufacturer has offered to sell frames to Frandec for $45.00 each. Could Frandec improve its position by pursuing this opportunity? Why or why not?

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