A company manufactures two types of chemicals A and B. Each chemical requires two types of raw material P and Q. The table below shows number of units of P and Q required to manufacture one unit of A and one unit of B and the total availability of P and Q.
| Raw Material | A | B | Availability |
|---|---|---|---|
| P | 3 | 2 | 120 |
| Q | 2 | 5 | 160 |
The company gets profits of Rs.350 and Rs.400 by selling one unit of A and one unit of B respectively. (Assume that the entire production of A and B can be sold). How many units of the chemicals A and B should be manufactured so that the company get maximum profit? Formulate the problem as L.P.P. to maximize the profit.
Let = units of chemical A and = units of chemical B manufactured. Let = units of A, = units of B. The non-negativity constraints are since a negative quantity produced has no meaning. Raw material P (3 units/A, 2 units/B) is capped at 120 units and Q (2 units/A, 5 units/B) at 160 units; profit is Rs.350 per unit of A and Rs.400 per unit of B, sold entirely as assumed. (The exact production quantities that maximize profit would be found by the corner-point method of section 7.2.3, which this section has not yet introduced — only the formulation is asked here.)
The L.P.P. is — Maximize: subject to .
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