A contractor builds two models of homes, model A and model B. The model A requir
ID: 2407438 • Letter: A
Question
A contractor builds two models of homes, model A and model B. The model A requires 500 worker-days of labor and $500,000 in capital, and model B requires 300 worker-days of labor and $150,000 in capital. The contractor has a total of 7500 worker-days and $4,500,000 in capital available per month. The profit is $150,000 on model A and $45,000 on model B. Building how many of each model will maximize the monthly profit? What is the maximum possible profit? Building how many of each model will maximize the monthly profit? Choose the correct answer below. 0 A. Profit is maximized with 0 models of A and 9 models of B, with 20 models of A and 3 models of B, or with 10 models of A and 6 models of B 0 B. Profit is maximized with 0 models of A and 9 models of B, with 20 models of A and 3 models of B, or with 6 models of A and 10 models of B ° C. Profit is maximized with 9 models of A and 0 models of B, with 3 models of A and 20 models of B, or with 6 models of A and 10 models of B. O D. Profit is maximized with 0 models of A and 9 models of B, with 3 models of A and 20 models of B, or with 6 models of A and 10 models of B. The maximum possible profit will be SExplanation / Answer
In the given case we have limited resources in terms of labour & capital available per month.
Therefore, we need to find out profit per unit of resource in both the models
$300
(150000 / 500)
$150
(45000 / 300)
$0.3
($150000/ 500000)
$0.3
($45000 / 150000)
Since the profit per $ of capital requirement is same, we shall take the decision on the basis of profit per worker day.
Looking at the above table, profit per worker day is higher for model A & therefore model A should definitely be built
As per the decision, Option C should be chosen because
1. When 9 models of A are built & 0 models of B then
Profit for A = 9 * $ 150000 = $1350000
Profit for B = 0
Total Profit = $150000
2. When 3 models of A & 20 models of B are built then
Profit for A = 3 *$150000 = $450000
Profit for B = 20 * $45000 = $900000
Total Profit = $1350000
3. When 6 models of A & 10 models of B are built then
Profit for A = 6 * $150000 = $900000
Profit for B = 10 * $45000 = $450000
Total Profit = $1350000
Also, under all the situation of Option C the resources are utilized optimally to the fullest.
Conclusion: Option C sholud be chosen & as seen from the above calculation maximum profit shall be $1350000
Particulars Model A Model B Profit as given $150000 $45000 Worker days required 500 300 Profit per worker day$300
(150000 / 500)
$150
(45000 / 300)
Capital required $500000 $150000 Profit per $ of capital$0.3
($150000/ 500000)
$0.3
($45000 / 150000)
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