A paper mill produces paper rolls in two standard widths; one with width 20 in. and the other with width 50 in. It is desired to produce new rolls with different widths as indicated below. The new rolls are to be produced by cutting the rolls of standard widths to minimize the trim loss. Formulate the problem as an LP problem.

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STANDRD Roll widths\mathrm{Nb} of rollsWidtn(inch)40150152006\frac{50}{100}Now(1) for Roll \rightarrow 40 inch. Width only Possibility to cut from is 50 in. roll.let no of so inch ools ter this x50 x_{1}=40 \times 150=6000(2) for roll \rightarrow 30 inch widen wt \rightarrow 50 inch. Roll x_{2}50 x_{2}=30 \times 200=6000(3) for 15 irch rell.20 x_{3}+50 x_{4}=15 \times 50=750(4) for b in roll.again\begin{array}{ll}\sqrt{1} \text { (20ixeh } & x_{6}(50 \text { inch) } \\20 x_{5}+50 x_{6}=6 \times 100=600\end{array}Now Total no of roolls (20ish net excecd. 10 tal no of Dolls reguived\begin{array}{l} \therefore\left(x_{1}\right.+x_{2}+x_{3}+x_{4} \\\left.+x_{5}+x_{6}\right) \leq 150+200+50 \\+100 \\\left(x_{1}+x_{2}+x_{3}+x_{4}+x_{5}+x_{6}\right) \leq 500\end{array} ...