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Exercise 7.3 · Q30
Q.

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 :

GadgetsFoundryMachine Shop
A105
B64
Time available (hour)6035

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.

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✓ Free question

Let xx = number of units of gadget A and yy = number of units of gadget B produced. Let xx = units of A, yy = units of B. The non-negativity constraints are x≥0,y≥0x\ge0, y\ge0 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.

✓Final answer

The L.P.P. is — Maximize: Maximize z=30x+20y\text{Maximize } z = 30x + 20y subject to 10x+6y≤60 (foundry), 5x+4y≤35 (machine shop), x≥0, y≥010x+6y\le60 \text{ (foundry)},\ 5x+4y\le35 \text{ (machine shop)},\ x\ge0,\ y\ge0.

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