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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. |
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Answer» 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` `Rightarrowx-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` |
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