Optimization Questions

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:

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.

A cricket bat manufacturing firm assesses its variable cost to be $2x(x-40)$, where $x$ is the number of bats produced, and the fixed cost incurred on storage is $Rs.1200$. How many bats should be manufactured for the minimum total cost?

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

The number that exceeds its square by the greatest amount is:

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:

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.