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Product Mix Decision under Capacity Constraint
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When a concern manufactures more than one product, a problem often arises as to the product mix or the sales mix which will yield the maximum profits. In determining the optimum or profitable sales mix, the products, that give the maximum contribution are to be retained and their production should be increased. The production of products, which give comparatively lesser contribution, should be reduced or dropped altogether.
Illustration
A confectioner markets three products, all of which require sugar. His average monthly sales, cost of sales and sugar consumption are as follows:
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Product A
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Product B
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Product C
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Total
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Sales (Rs.)
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1,00,000
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1,20,000
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80,000
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3,00,000
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Cost of Sales (Rs.)
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60,000
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80,000
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56,000
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1,96,000
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Sugar Requirement (kg.)
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5,000
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8,000
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2,400
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15,400
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Due to government restrictions, his sugar quota has been reduced to 14,500 kg. per month. Suggest a suitable sales mix, which would give the confectioner maximum profit under the given circumstances.
Solution
Availability of sugar is the limiting factor; so we have to find out profit per kg of sugar in case of each product, to determine the profitability of various products.
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Particulars
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Product A
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Product B
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Product C
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Sales (Rs.)
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Rs.1,00,000
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1,20,000
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80,000
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Less: Cost of sales (Rs.)
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Rs.60,000
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80,000
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56,000
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Profit (Rs.)
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Rs.40,000
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40,000
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24,000
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Sugar requirement (kgs.)
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5,000
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8,000
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2,400
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Profit per kg of sugar (Rs.)
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8
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5
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10
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If we see profit per kg of sugar we come to the conclusion that product B is the least advantageous product and product A and Product C should be given preference over product B.
Sugar quota is 14,500 kg. whereas present requirement of sugar is 15,400 kg. Therefore, present sales of all product cannot be continued, sales of least profitable product B should be reduced to cope with the shortage of sugar. Then the suitable sales mix is:
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Particulars
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Sales
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Sugar requirement (kgs.)
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Product A
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1,00,000
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5,000
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Product C
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80,000
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2,400
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Product B
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1,06,500
[(7100/8000) * 1,20,000]
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7,100
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(14,500 - 7,400)
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