The maximum value of $z=7x+8y$ subject to the constraints $x+y \leq 20, y \geq 5, x \leq 10, x \geq 0, y \geq 0$ is

For the Linear Programming Problem ($L$.$P$.$P$.),maximize $z = 4x_1 + 2x_2$ subject to the constraints $3x_1 + 2x_2 \geq 9$,$x_1 - x_2 \leq 3$,$x_1 \geq 0$,$x_2 \geq 0$,the problem has:

The maximum value of the objective function $z=4x+6y$ subject to the constraints $3x+2y \leq 12$,$x+y \geq 4$,$x, y \geq 0$ is

The minimum value of $z = 3x + 5y$, subject to constraints $x \leq 80$, $y \geq 60$, $x + y \leq 200$, $x, y \geq 0$ occurs at the point...

The maximum value of $2x + y$ subject to $3x + 5y \leq 26$ and $5x + 3y \leq 30, x \geq 0, y \geq 0$ is

$A$ manufacturer produces two models of bikes: Model $X$ and Model $Y$. Model $X$ takes $6$ man-hours to make per unit,while Model $Y$ takes $10$ man-hours per unit. There is a total of $450$ man-hours available per week. Handling and marketing costs are $Rs. 2000$ and $Rs. 1000$ per unit for Models $X$ and $Y$ respectively. The total funds available for these purposes are $Rs. 80,000$ per week. Profits per unit for Models $X$ and $Y$ are $Rs. 1000$ and $Rs. 500$ respectively. How many bikes of each model should the manufacturer produce so as to yield a maximum profit? Find the maximum profit.