The manufacturing company can sell a maximum of 10,000 units of a product, which
ID: 3120547 • Letter: T
Question
The manufacturing company can sell a maximum of 10,000 units of a product, which are quality approved. The company has 3 processing plants, each with a processing capacity of 5000 units, costs of processing and percentage of rejections varies for various plants. The only cost other than processing cost is raw material, which is $ 200 per unit. All quality approved goods are sold for $ 600 each and rejections are solid per $ 50 each. The company has policy of not having more than overall 3% rejections. Formulate LP model to decide optimum production by various plants.Explanation / Answer
Let x, y and z be the number of units of product produced by 3 different manufacturing plants A, B and C respectively.
Demand of number of units of products = 10000
0.95x + 0.97y + 0.98z <= 10000 (requirement of quality approved products)
Not more than 3% of rejections,
0.05x + 0.03y + 0.02z <= 0.03(x+y+z)
0.02x - 0.01z <= 0
Capacity constraint:
x <= 5000
y <= 5000
z <= 5000
Profit P can be given by
P = 600*(0.95x + 0.97y + 0.98z) + 50*(0.02x - 0.01z) - (100x + 125y + 150z + 200*(x+y+z) )
P = 271x + 357y + 237.5z
Hence the LPP can be formulated as below,
max Z = 271x + 357y + 237.5z
subject to,
0.95x + 0.97y + 0.98z <= 10000
0.02x - 0.01z <= 0
x <= 5000
y <= 5000
z <= 5000
The optimal solution value is Z = 3105240.5498282
x = 1769.7594501718 = 1770
y = 5000
z = 3539.5189003436 = 3540
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