A manufacturing firm produces two types of gadgets A and B, which are first processed in the foundry and then sent to machine shop for finishing. The number of man hours of labour required in each shop for production of A and B per unit and the number of man hours available for the firm are as follows :
| Gadgets | Foundry | Machine Shop |
|---|---|---|
| A | 10 | 5 |
| B | 6 | 4 |
| Time available (hour) | 60 | 35 |
Profit on the sale of A is Rs. 30 and B is Rs. 20 per units. Formulate the L.P.P. to have maximum profit.
Let = number of units of gadget A and = number of units of gadget B produced. Let = units of A, = units of B. The non-negativity constraints are since a negative quantity produced has no meaning. The foundry uses 10 man-hours per unit of A and 6 per unit of B, capped at 60 hours; the machine shop uses 5 hours per unit of A and 4 per unit of B, capped at 35 hours; profit is Rs.30 per A and Rs.20 per B.
The L.P.P. is — Maximize: subject to .
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