Optimization Questions

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?