A company manufactures two types of screws A and B. all the screws have to pass through a threading machine and a slotting machine. A box of type A screw requires 2min on the threading machine and 3 min on the slotting machine. A box of type B screw requires 8 min on the threading machine and 2 min on the slotting machine. In a week each machine is availbale for 60h. On selling these screws, the company gets a profit of 100 box on type A screw and 170 per box on type B screws. Formulate this problem as a LPP given that the objective is to maximise profit.

Answer

N/a

Explanation

Let the company manufactures x boxes of types A screws and y boxes of types B screws From the given information, we have following corresponding constraint table

Thus, we see that objective function for maximum proft is Z=100x+170y
Subject to constraints
`2x+8y le 60 xx 60 ["time constraints for threading machine"]`
`Rightarrow x+4y le 1800..(i) `
and `3x+2y le 60xx60["time constraint for slotting machine"]`
`Rightarrow 3x+2y le 3600....(ii)`
Also, `x ge 0, y ge 0 ["non negative contraints"] ...(iii)`
`therefore "Required LPP is"`
Maximise `Z=100x+170y`
Subject to constraints `x+4y le 1800, 3x+2y le 3600, x ge 0, y le 0`,