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A firm produces three products P_{v}, P_{2} and P_{1} requiring the mixup of four materials M_{D}, M_{D}, M and M_{d} The matrix below gives the amount of material needed for each product: MA A=P 1 [ [[2, 3, 1, 12], [7, 9, 5, 20], [P_{3}, 0, 0, 0]] [ matrix 8&12&6&15 matrix ]. Using matrix notations, find (i) the total requirement of each material if the firm produces 70 units of P,, 120 units of P_{2} and 50 units of P (ii) the per unit cost of production of each product if the per unit costs of materials M_{1}, M_{2}, M_{3} and M * are 10, 12, 15 and 20 respectively, and

Question

A firm produces three products P_{v}, P_{2} and P_{1} requiring the mixup of four materials M_{D}, M_{D}, M and M_{d} The matrix below gives the amount of material needed for each product: MA A=P 1 [ [[2, 3, 1, 12], [7, 9, 5, 20], [P_{3}, 0, 0, 0]] [ matrix 8&12&6&15 matrix ]. Using matrix notations, find (i) the total requirement of each material if the firm produces 70 units of P,, 120 units of P_{2} and 50 units of P (ii) the per unit cost of production of each product if the per unit costs of materials M_{1}, M_{2}, M_{3} and M * are 10, 12, 15 and 20 respectively, and

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Solution

The text you provided seems to be a bit jumbled and some parts are not clear. However, I'll try to provide a general approach to solve such problems.

(i) To find the total requirement of each material, you need to multiply the production matrix by the quantity matrix. The production matrix is given in the problem and the quantity matrix would be a column matrix of the quantities of each product, i.e., [70, 120, 50].

(ii) To find the per unit cost of production of each product, you need to multiply the cost matrix by the production matrix. The cost matrix would be a row matrix of the costs of each material, i.e., [10, 12, 15, 20].

Please provide the correct and complete matrix so that I can provide a more accurate solution.

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