CBSE Class 12-science Answered
A shopkeeper wants to sell T.V.and Refrigerators.A Refrigerator costs him 20000 Rs and a T.V. costs him 10000 Rs. He has 300000 Rs to invest.To maintain his dealership he must sell at least 3 Refrigerators and he can sell atmost 9 T.V. he has 24 sq unit of area to accommodate them. If a refrigerator requires 1 squnit and a T.V. requires 2 sq unit , find how many units of eachshould be kept so as to maximize the profit.
Asked by Topperlearning User | 18 Sep, 2014, 03:28: PM
Expert Answer
We have to maximize z = 4x + 8y
According to constraints, we have,
2x + y £ 30 ;
x + 2y £ 24;
x ³ 3 ;
y £ 9
x and y ³ 0.
Plotting these inequations on graph, we get shaded portion as the optimum solution.
Possible point for the maximum Z are A (3, 0), B (15, 0), C (12, 6), D (6, 9) and E (3, 9).
Let us tabulate the values of z at all the corner points.
Here, Z is maximum at C (12, 6) and D (6, 9).
Therefore, Z is maximum for x = 12, y = 6 or x = 6, y = 9.
Answered by | 18 Sep, 2014, 05:28: PM
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