Linear Programming Questions

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. 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 $A,B$)

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 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 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?

The activities or limitations competing with one another to share the amount of resources in linear programming are called:

The number of solutions in a linear programming model to maximize $5x+4y$ subject to $x-2y\ge 2$, $2x-4y\le -3$, and $x,y\ge 0$ will be:

Durgesh works in a restaurant preparing two types of dishes, A and B. Dish A takes 20 minutes to prepare and Dish B takes 30 minutes. He earns Rs 50 for dish A and Rs 70 for dish B. He works for 12 hours a day and needs 1 hour for personal activities. What will be the time constraint if formulated as a linear programming problem? Assume $x$ and $y$ are the packets of dishes A and B respectively.

The maximum value of the objective function $Z=4x+3y$ subject to $4x+2y\le 12$, $2x+4y\ge 6$, $x\ge 0,y\ge 0$ is:

Two models, $P$ and $Q$, of a product earn profits of $₹100$ and $₹80$ per piece, respectively. Production times for $P$ and $Q$ are $5$ hours and $3$ hours, respectively, while the total production time available is $150$ hours. For a total batch size of $40$, the objective function $Z$ is subjected to the constraints:

Maximize $z=4x_1+3x_2$ subject to constraints:$2x_1+x_2\le 1000$$x_1+x_2\le 800$$x_1\le 400$$x_2\le 700$$x_1,x_2\ge 0$ Find the optimum units of $x_1$ and $x_2$ to be used.

Consider the Linear Programming problem:Maximize: $7X_1+6X_2+4X_3$ subject to:$X_1+X_2+X_3\le 5$$2X_1+X_2+3X_3\le 10$$X_1,X_2,X_3\ge 0$ The number of basic solutions is:

Maximize $z=5x_1+3x_2$ subject to the following constraints:$x_1+x_2\ge 3$$x_1-x_2\le 2$ and the solution is in the first quadrant ($x_1,x_2\ge 0$). What can be said about the solution of this LPP?

The minimum value of $z=5x-7y$, subject to the constraints $x+y\le 7$, $2x-3y+6\ge 0$, $x\ge 0,y\ge 0$, is:

A manufacturer produces two types of products, 1 and 2, at production levels of $x_1$ and $x_2$ respectively. The profit is $2x_1+5x_2$. Constraints are $x_1+3x_2\le 40$, $x_1+x_2\le 10$, $x_1\ge 0,x_2\ge 0$. The maximum profit is:

The minimum value of $3x+5y$ such that:$3x+5y\le 15$$4x+9y\le 18$$13x+2y\le 2$$x\ge 0,y\ge 0$ is:

For the linear programming problem:$\text{Maximize }Z=3X_1+2X_2$ Subject to:$-2X_1+3X_2\le 9$$X_1-5X_2\ge -20$$X_1,X_2\ge 0$ The above problem has:

For a Linear Programming Problem, $Z=2x+4y$. Feasible corner points are $O(0,0),A(0,2.5),B(3,1),C(4,0)$. What is the optimal maximized value of $Z$?

Maximize $Z=2X_1+3X_2$ subject to $2X_1+X_2\le 6$, $X_1-X_2\ge 3$, $X_1,X_2\ge 0$. The solution to the LPP is:

Ram is a fruit seller. Apples cost Rs 80/kg and Mangoes Rs 120/kg. Profits are Rs 10/kg and Rs 12/kg respectively. Let $x$ be kgs of apples and $y$ be kgs of mangoes. If Ram wants to maximize profit, the objective function $Z$ is:

Maximize $Z=5x+8y$, subject to $2x+3y\ge 10$, $5x+2y\ge 14$, and $x,y\ge 0$. For this LPP:

Shyam needs a minimum of 150 units of carbohydrates and 120 units of proteins. Product A provides 16 units of carbohydrates and 11 units of proteins, while product B provides 10 units of carbohydrates and 20 units of proteins. The cost of product A is $₹50$ and product B is $₹60$. Formulate this situation as a Linear Programming Problem where $x$ and $y$ are units of products A and B respectively.

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.