A company manufacutres two types of sweaters type A and type B. It costs 360 to make type A sweater and 120 to make a type B sweater. The company can make atmost 300 sweater and spent atmost 72000 a day. The number of sweaters of type B cannot exceed the number of sweaters of type A by more than 100. The company makes a profit of 200 for each sweater of type A and 120 for every sweater of type B. Formulate this problem as a LPP to maximise the profit to the company.

Answer

N/a

Explanation

Let the company manufactures x number of type A sweaters and y number of type B sweaters. From the given information we see that cost to make a type A sweater is 360 and cost to make type B sweater is 120.
Also, the company spend atmost 72000 a day
`therefore 360x+120 le 72000`
`Rightarrow 3x+y le 600...(i)`
Also, company can make atmost 300 sweaters.
`x+y le 300....(ii)`
Further, the number of sweaters of type B cannot exceed the number of sweater of type A by more than 100 i.e.
`x+100 ge y`
`Rightarrow x-y ge -100 ...(ii)`
Also, we have have non-negative constraints for x and y i.e. `x ge 0, x ge 0, y ge 0, ....(iv)`
Hence, the company makes a profit fo 200 each sweater of type A and 120 for each sweater of type B i.e.
Profit (Z)=200x+120y
Thus, the required LPP to maximise profit is
Maximise Z=200x+120y is subjected to constraints.
`3x+y le 600`
`x+y ge300`
`x-y ge -100`
`x ge 0, y ge 0`