A firm manufactures two types of products, $A$ and $B$, and sells them at a profit of $\approx 2$ on type $A$ and B. Each product is processed on two machines, $M_{1}$ and $M_{2}$. Type A requires one minute of processing time on $M_{1}$ and two minutes on $M_{2} .$ Type $B$ requires one minute on $M_{1}$ and one minute on $M_{2}$ is available for not more than 6 hours 40 minutes while $M_{2}$ is available for at most 10 hours a day. Find how many products of each type the firm should produce each day in order to get maximum profit.

Home » A firm manufactures two types of products, and , and sells them at a profit of on type and B. Each product is processed on two machines, and . Type A requires one minute of processing time on and two minutes on Type requires one minute on and one minute on is available for not more than 6 hours 40 minutes while is available for at most 10 hours a day. Find how many products of each type the firm should produce each day in order to get maximum profit.

A firm manufactures two types of products, $A$ and $B$ , and sells them at a profit of $\approx 2$ on type $A$ and B. Each product is processed on two machines, $M_{1}$ and $M_{2}$ . Type A requires one minute of processing time on $M_{1}$ and two minutes on $M_{2} .$ Type $B$ requires one minute on $M_{1}$ and one minute on $M_{2}$ is available for not more than 6 hours 40 minutes while $M_{2}$ is available for at most 10 hours a day. Find how many products of each type the firm should produce each day in order to get maximum profit.

A firm manufactures two types of products, $A$ and $B$ , and sells them at a profit of $\approx 2$ on type $A$ and B. Each product is processed on two machines, $M_{1}$ and $M_{2}$ . Type A requires one minute of processing time on $M_{1}$ and two minutes on $M_{2} .$ Type $B$ requires one minute on $M_{1}$ and one minute on $M_{2}$ is available for not more than 6 hours 40 minutes while $M_{2}$ is available for at most 10 hours a day. Find how many products of each type the firm should produce each day in order to get maximum profit.

Let the firm manufacture $x$ number of Aand y number of $B$ products.
$\therefore$ According to the question,
$X+y \leq 400,2 x+y \leq 600, x \geq 0, y \geq 0$
Maximize $Z=2 x+2 y$
The feasible region determined by $\mathrm{X}+\mathrm{y} \leq 400,2 x+y \leq 600, x \geq 0, y \geq 0$ is given by

The corner points of feasible region are $A(0,0), B(0,400), C(200,200), D(300,0) .$ The value of $Z$ at corner point is

The maximum value of $Z$ is 800 and occurs at two points. Hence the line $B C$ is a feasible solution. The firm should produce 200 number of Aproducts and 200 number of B products.

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