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A company produces cars at three different plants in amounts x, y and z, respectively,producing an annual revenue of f(x, y, z) = x2yz − 2(x + y + z). The company is toproduce 100 units annually. How should the production be distributed to maximizethe revenue? Solve this problem by using the Lagrange multiplier method. |
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Answer» (a) The unit sale prices of x,y and z are respectivelyRs.2.50,RS.1.50 and Rs.1.00. Total revenue in market I can be represented as: [10000200018000]⎣⎢⎢⎡2.501.501.00⎦⎥⎥⎤ =10000×2.50+2000×1.50+18000×1.00 =25000+3000+18000 =46000 Total revenue in market II can be represented as: [6000200008000]⎣⎢⎢⎡2.501.501.00⎦⎥⎥⎤ =6000×2.50+20000×1.50+8000×1.00 =15000+30000+8000 =53000 So, the total revenue in market I is Rs 46000 and in market II is Rs.53000. (B) The unit cost prices of x,y and z are respectively given as Rs.2.00, Rs. |
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