Question

Larkin Industries manufactures several lines of decorative and functional metal items. The most recent order has been for 1200 door lock units for an apartment complex developer. The sales and production departments must work together to determine delivery schedules. Each lock unit consists of three components: the knob and face plate, the actual lock itself, and a set of two keys. Although the processes used in the manufacture of the three components vary, there are three areas where the production manager is concerned about the availability of resources. These three areas, their usage by the three components, and their availability are detailed in the table.

Resource	Knob and Plate	Lock	Key (each)	Available
Brass Alloy	12	5	1	15000 units
Machining	18	20	10	36000 minutes
Finishing	15	5	1	12000 minutes

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A quick look at the amounts available confirms that Larkin does not have the resources to fill this contract. A subcontractor, who can make an unlimited number of each of the three components, quotes the prices below.

Component	Subcontractor Cost	Larkin Cost
Knob and Plate	10.00	6.00
Lock	9.00	4.00
Keys (set of 2)	1.00	.50

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Develop a linear programming model that would tell Larkin how to fill the order for 1200 lock sets at the minimum cost.

Develop the objective function and constraints then solve the problem using Excel or Mgt. Scientist. Solving the problem is worth 5 points extra credit.

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Let PM = the number of knob and plate units to make PB = the number of knob and plate units to buy LM = the number of lock units to make LB = the number of lock units to buy KM = the number of key sets to make KB = the number of key sets to buy Min Objective Function: s.t. Constraints: Hint: There are 6 constraints (in addition to the non negativity constraint) 3 constraints are for the availability of resources, brass alloy, machining and finishing. 3 are for the amount of sets required, i.e., at least 1200 plates, 1200 locks, and 1200 key sets. PM, PB, LM, LB, KM, KB ≥ 0 You receive 5 points extra credit for providing the total cost and the amounts of each to make and buy. In other words, by solving the linear program, you will receive the extra credit points. Total Cost: Amount to make of each Amount to buy of each

Answer 1

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