MHT CET 2025 26th April Evening Shift | Linear Programming Question 1 | Mathematics

A manufacturing company produces two items, A and B. Each toy should be processed by two machines, I and II. Machine I can be operated for maximum 10 hours 40 minutes. It takes 20 minutes for an item of A and 15 minutes for B. Machine II can be operated for a total time at 8 hours 20 minutes. It takes 5 minutes for an item A and 8 minutes for B . The profit per item of $A$ is $Rs 25$ and per item of $B$ is ₹ 18 . The formulation of an L.P.P. to maximize the profit (where $x$ is number of items A and $y$ is the number of item $B$ ) is

$$ \begin{aligned} & \text { Maximize } \mathrm{z}=25 x+18 y \\ & \text { subject to } 20 x+15 y \leq 640 \\ &\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, 5 x+8 y \geq 500 \\ &\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, x, y \geq 0 \end{aligned} $$

Maximize $z=25 x+18 y$

$$ \begin{aligned} \text { subject to } 20 x+15 y & \leq 640 \\ 5 x+8 y & \leq 500 \\ x, y & \geq 0 \end{aligned} $$

$$ \begin{array}{r} \text { Maximize } z=25 x+18 y \\ \text { subject to } 20 x+5 y \leq 8 \\ 5 x+8 y \leq 10 \\ x, y \geq 0 \end{array} $$

$$ \begin{aligned} & \text { Maximize } \mathrm{z}=25 x+18 y \\ & \text { subject to } 4 x+3 y \leq 128 \\ & \qquad \begin{array}{r} 5 x+8 y \geq 500 \\ x, y \geq 0 \end{array} \end{aligned} $$

MHT CET 2025 26th April Morning Shift

MCQ (Single Correct Answer)

-0

The solution for minimizing the function $\mathrm{z}=x+y$ under an L.P.P. with constraints $x+y \geq 2, x+2 y \leq 8, y \leq 3, x, y \geq 0$ is

at the point $(0,3)$

at the point $(8,0)$

at infinite number of points but bounded set

at unbounded set

MHT CET 2025 25th April Evening Shift

MCQ (Single Correct Answer)

-0

In L.P.P., the maximum value of objective function $\mathrm{Z}=6 x+3 y$ subject to constraints $x+y \leq 5, x+2 y \geq 4,4 x+y \leq 12, x, y \geq 0$ is

$\frac{132}{7}$

$\frac{122}{7}$

MHT CET 2025 25th April Morning Shift

MCQ (Single Correct Answer)

-0

The solution set of the constraints $|x-y| \leq 1, x, y \geq 0$ is

a finite set

an unbounded set

a convex polygon

such that feasible region does not exist

MHT CET Subjects