$\begin{array}{1 1}(A)\;z=120x+200y \\ (B)\;z=360x+120y \\ (C)\;z=200x+120y \\(D)\;z=120x+360y \end{array} $

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- Let $R$ be the feasible region for a linear programming problem and let $z=ax+by$ be the objective function.When $z$ has an optimum value (maximum or minimum),where variables $x$ and $y$ are subject to constraints described by linear inequalities,this optimum value must occur at a corner point of the feasible region.
- If R is bounded then the objective function Z has both a maximum and minimum value on R and each of these occur at corner points of R

Step 1:

For type A: No of sweaters=360.Cost per sweater is 200.

For type B: No of sweaters=100.Cost per sweater is 120.

Maximum cost =72000.

Step 2:

Let $x$ be number of sweaters of type A and $y$ be the number of sweaters of type B.

These sweaters are brought to fulfill the maximum requirement of $x,y$ and maximize the profit.

Step 3:

The mathematic formulation of the above problem is as follows :

Maximize $z=200x+120y$

Subject to $360x+120y\leq 72,000$

$\Rightarrow 3x+y\leq 600$

$x+y\leq 300$

$y-x \leq 100$ and $x\geq 0$ and $y \geq 0$

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