Linear Programming Questions

Consider the constraints:$5x+y\le 100$$x+y\le 60$$x\ge 0,y\ge 0$ Solving by graphical method, which point among the following will not form a boundary/corner point of the feasible region?

Which among the following is not a property of a Linear Programming Problem (LPP)?

Durgesh is working in a restaurant in which he prepares two types of dishes $A$ and $B$. Dish $A$ takes 20 minutes to be prepared and Dish $B$ takes 30 minutes for the same. He earns Rs 50 to make one packet of dish $A$, while Rs 70 for one packet of dish $B$. He works for 12 hours a day, including 1 hour for personal activities. What will be the objective function if this example is formulated as a linear programming problem? Assume $x$ and $y$ are the packets of dishes $A$ and $B$ respectively.

Consider the objective function $z=3x+4y$ subject to $4x+3y\le 24$, $3x+4y\le 24$, and $x,y\ge 0$. The objective function $z$ is maximized:

Durgesh is working in a restaurant in which he prepares two types of dishes $A$ and $B$. Dish $A$ takes 20 minutes to be prepared and Dish $B$ takes 30 minutes. He earns Rs 50 to make one packet of dish $A$ and Rs 70 for dish $B$. He works for 12 hours a day, using 1 hour for personal activities. What will be the objective function to maximize his earnings? (Let $x,y$ be packets of $A,B$)

Maximize $Z=4x+6y$ subject to $3x+2y\le 12$, $x+y\ge 2$, $x,y\ge 0$.

An objective function $Z=ax+by$ is maximum at points $(9,3)$ and $(5,7)$. If $a,b\ge 0$ and $ab=16$, then the maximum value of the function is:

Which of the following is one of the feasible solutions for a Linear Programming Problem with constraints: $x+2y\ge 2$, $5x+4y\le 20$, $2x-y\le 4$, $x\ge 0$, $y\ge 0$?

For an objective function $Z=x+y$ with constraints $2x+2y\le 5$ and $4x-3y\ge 3$ ($x,y\ge 0$), at what point(s) will $Z$ achieve its maximum value?

Maximize $Z=30x-18y$ subject to $3x+4y\le 60$ and $5x-3y\le 20$ ($x,y\ge 0$). In the feasible region, the maximum value occurs at:

The point that lies in the region bounded by the lines $7x+y\ge 40$ and $2x+3y\le 25$ is:

Ashok bought tables and chairs for a marriage hall. The cost of a table is $₹2500$ and a chair is $₹500$. He has a budget of $₹60000$ and space for at most $60$ items. If the profit is $₹75$ per table and $₹25$ per chair, find the maximum profit.