Question

Suppose a firm produces two products X1 and X2. Each unit of product X1 contributes Rs. 30 to profit and each unit of product X2 contributes Rs. 40 to profit. The production of these products requires inputs A and B and their available quantities are 14 and 10 units respectively. It is given that production of one unit of product X1 requires 2 units of input A, 1 unit of input B. The production of one unit of product X2 requires 2 units of input A, 2 units of input B.​

Answer 1

Answer:

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Answer 2

Given the data of a company producing two products, find the profit for the given available number of input units

Explanation:

1. let the number of product units of both the products 'X1' and 'X2'  be 'x' and 'y' respectively then the total profit 'P' is,  $P=30x+40y$  
2. given that X1 uses input units as ,  $2-A\ units\ \ \ \ \ \ 1-B\ unit$                                given that X2 uses input units as,  $2-A\ units\ \ \ \ \ \ 2-B\ units$
3. then the available number of input units of 'A'  is given by,                                       $2x+2y=14\ \ \ \ \ -> x+y=7$     -----(a)
4. then the available number of input units of 'B' is given by,                                  $x+2y=10$                                                                                                               from (a) we get, [tex]y=10-7\ \ \ \ \ ->y=3\\ x=10-3\ \ \ \ \ ->x=7 [/tex]        
5. putting these value in equation of total profit we get,                                     [tex]P=30(7)+40(3)\\ P= Rs.\ 330 [/tex]         ------->ANSWER