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14. Sanja and Co. manufactures toys and sells at three places, Agra, Benguluru and Chennai by using three raw materials P, Q and R. The profit on a toy varies as f(x) = n(x² - 2x + 3), where x is the number of toys produced and n is the profit index at a given place. The information related to this manufacture is given in the following table. Formulate the problem. Raw material P Q R Profit index Agra 8 4 2 20 Benguluru 3 1 6 Chennai 3 1 1 8 Available units per week 250 150 100

14. Sanja and Co. manufactures toys and sells at three places, Agra, Benguluru and Chennai by using three raw materials P, Q and R. The profit on a toy varies as f(x) = n(x² - 2x + 3), where x is the number of toys produced and n is the profit index at a given place. The information related to this manufacture is given in the following table. Formulate the problem. Raw material P Q R Profit index Agra 8 4 2 20 Benguluru 3 1 6 Chennai 3 1 1 8 Available units per week 250 150 100

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
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14. Sanja and Co. manufactures toys and sells at three places, Agra, Benguluru and Chennai by using three raw materials P, Q and R. The profit on a toy varies as f(x) = n(x² - 2x + 3), where x is the number of toys produced and n is the profit index at a given place. The information related to this manufacture is given in the following table. Formulate the problem. Raw material P Q R Profit index Agra 8 4 2 20 Benguluru 2 3 1 6 Chennai 3 1 1 8 Available units per week 250 150 100
Transcribed Image Text:14. Sanja and Co. manufactures toys and sells at three places, Agra, Benguluru and Chennai by using three raw materials P, Q and R. The profit on a toy varies as f(x) = n(x² - 2x + 3), where x is the number of toys produced and n is the profit index at a given place. The information related to this manufacture is given in the following table. Formulate the problem. Raw material P Q R Profit index Agra 8 4 2 20 Benguluru 2 3 1 6 Chennai 3 1 1 8 Available units per week 250 150 100
Expert Solution
Step 1: Define the variables

Let x,y and z be the numbers of toys produced at Agra, Bengaluru and Chennai respectively.

Profit on a toy at Agra=20(x2−2x+3)

Profit for x toys=20x(x2−2x+3)

Profit on a toy at Bengaluru =6(y2−2y+3)

Profit for y toys=6y(y2−2y+3)

Profit on a toy at Chennai =8(z2−2z+3)

Profit for z toys=8z(z2−2z+3)

The raw materials P, Q and R can be use maximum 250, 150 and 100 units for production of toys respectively.

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