# Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers. One...

Frandec Company manufactures, assembles, and rebuilds material handling 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's production schedule calls for 6000 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown. Component Frame Support Strap Manufacturing Cost \$39.00 \$12.50 \$7.50 Purchase Cost \$52.00 \$16.00 \$8.50 Three departments are involved in the production of these components. The time in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows: Department Milling 2.3 Cutting 3.6 1.4 Component Frame Support Strap Capacity (hours) Shaping 3.2 1.8 0.9 2.7 1.8 690 370 430 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? Let FM = number of frames manufactured FP = number of frames purchased SM = number of supports manufactured SP = number of supports purchased TM = number of straps manufactured
TP = number of straps purchased Min FM + FP SM + SP + TM + ТР s.t. FM SM TM FM SM s FM SM + TM 3 1 FM + 1 FP 1 SM + 1 SP 1 TM + 1| VTP_2 5,000 X FM, FP, SM, SP, TM, TP 2 0 If required, round your answers to the nearest whole number. If an amount is zero, enter"0" Manufacture Purchase Purchani Frames 5,000 x Supports Straps b. What is the total cost of the manufacturing and purchasing plan? When required, round your answer to the nearest dollar. \$ 0 X
b. What is the total cost of the manufacturing and purchasing plan? When required, round your answer to the nearest dollar. \$ 0 x c. How many hours of production time are used in each department? If required, round your answer to two decimal places. Hours of production Department time used Cutting hours Milling hours Shaping hours d. How much should Frandec be willing to pay for an additional hour of time in the shaping department? If required, round your answers to the nearest whole number. If an amount is zero, enter "0". e. Another manufacturer has offered to sell frames to Frandec for \$46 each. Could Frandec improve its position by pursuing this opportunity? Yes Why or why not? If required, round your answers to the nearest cent. The reduced cost is \$ which means that the solution may be improved if the cost is Because the current purchase price is \$ \$ or below.

Based on the decision variables defined in the question,

Total Cost = 39*FM + 12.5*SM + 7.5*TM + 52*FP + 16*SP + 8.5*TP

We have to minimize this cost

Subject to constraints

3.6*FM + 1.4*SM + 0.9*TM <= 370 hours * 60 minutes i.e. 22200..........Constraint for availability of minutes of Cutting time

2.3*FM + 1.8*SM + 0*TM <= 430 * 60 = 25,800 .....................................Constraint for availability of minutes of Milling time

3.2*FM + 2.7*SM + 1.8*TM <= 690*60 = 41,400......................................Constraint for availability of minutes of Shaping time

Total Demand of final product = 6000 units

FM + FP >= 6000..........Constraint for demand of Frames

SM + SP >= 12000........Constraint for demand of Support (2 supports per 1 Liftmaster)

TM + TP >= 6000..........Constraint for demand of Strap

Hence, we get formulation as

Minimize Total Cost C = 39*FM + 12.5*SM + 7.5*TM + 52*FP + 16*SP + 8.5*TP

Subject to Constraints:

3.6*FM + 1.4*SM + 0.9*TM <= 22200

2.3*FM + 1.8*SM + 0*TM <= 25800

3.2*FM + 2.7*SM + 1.8*TM <= 41400

FM + FP >= 6000

SM + SP >= 12000

TM + TP >= 6000

FM, SM, TM, FP, SP, TP >=0

We solve in Excel using Excel solver as shown below:

The above solution in the form of formulas along with Excel Solver extract is shown below for better understanding and reference:

As seen from the above solution, we get

b. The total cost of manufacturing and purchasing plan = \$475,500

c. Hours used:

For part d and e, we generate a sensitivity report as shown below:

d. As seen from the above sensitivity report,

The shadow price for Shaping Department (Cell B15 in Constraints table) is 0. Hence, any increase in the number of hours in the shaping department will lead to a 0 decrease in total cost. Hence, 0 hours should be Frandec should be willing to pay \$0.

e. As seen from the above sensitivity report,

The Reduced cost for Frames to be purchased (Cell B5 in Variables table) is 4. In order to make the optimal solution such that Frames are purchased, the price of frames should be reduced by at least \$4 i.e. 52-4 = \$48. Since the supplier is supplier at \$46 which is less than minimum reduced price, Frandec can improve by pursuing this opportunity

Because the current purchase price is \$52. The reduced cost is \$4 which means that the solution may be improved if the cost is \$48 or below.

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