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LMN Ltd manufactures three products L, M and N. The company which supplies the two raw...

LMN Ltd manufactures three products L, M and N. The company which supplies the two raw materials which are used in all three products has informed LMN that their employees are refusing to work overtime. This means that supply of the materials is limited to the following quantities for the next period: Material A 1,030 kg Material B 1,220 kg No other source of supply can be found for the next period. Information relating to the three products manufactured by LMN Ltd is as follows: L M N Quantity of material used per unit manufactured: Material A (kg) 2 1 4 Material B (kg) 5 3 7 Maximum sales demand (units) 120 160 110 Contribution per unit sold £15 £12 £17.50 Owing to the perishable nature of the products, no finished goods are held. Requirements (a) Recommend a production mix which will maximise the profits of LMN Ltd for the forthcoming period. (b) LMN Ltd has a valued customer to whom they wish to guarantee the supply of 50 units of each product next period. Would this alter your recommended production plan?

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Expert Solution

(a)

L M N Total
Maximum sales demand (units) 120 160 110
Material A required per unit (kg) 2 1 4
Total material A required (kg) 240 160 440 840
Material B required per unit (kg) 5 3 7
Total material B required (kg) 1200 480 3080 4760

There is sufficient material A however, material B is the constraint.

L M N
Contribution per unit 15 12 17.5
Material B required per unit (kg) 5 3 7
Contribution per kg of material B 3 4 2.5
Ranking II I III

Since the contribution per kg of material B is highest for product M, maximum demand for the same will be first met then product L and the balance material B remaining will be used to produce product N.

Product Units Produced Material B used (kg)
M 160 480
L 120 600
N 20 140
Total 1220

(b) Yes. Since 50 units of product N are not produced, in order to satisfy the valued customers order for 50 units of each product, units of L produced will be reduced since it is second in ranking in order to produce more units of product N.

Product Units Produced Material B used (kg)
M 160 480
N 50 350
L 78 390
Total 1220

ekkarill92 answered 2 years ago
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