The maximum value of $z = 5x + 3y$ subject to constraints $3x + 5y \leq 15, x \geq 0, y \geq 0$ is :

The minimum value of $t = 7x + 3y$ subject to constraints $x + y < 5$,$x + y < 10$,$x > 0$,$y > 0$ is . . . . . .

If $Z = 7x + y$ subject to $5x + y \geq 5$,$x + y \geq 3$,$x \geq 0$,$y \geq 0$,then the minimum value of $Z$ is

$A$ scholarship amount is given by $z = 550x + 300y$ and is to be distributed among $x$ boys and $y$ girls. From the graph given below,the maximum amount of scholarship is . . . . . . .

The minimum value of $z = 2x + 4y$ subject to constraints $x + 2y \geq 10$,$3x + y \geq 10$,$x \geq 0$,$y \geq 0$ is $....$

$A$ company makes $3$ models of calculators: $A, B$ and $C$ at factory $I$ and factory $II.$ The company has orders for at least $6400$ calculators of model $A, 4000$ calculators of model $B$ and $4800$ calculators of model $C.$ At factory $I, 50$ calculators of model $A, 50$ of model $B$ and $30$ of model $C$ are made every day; at factory $II, 40$ calculators of model $A, 20$ of model $B$ and $40$ of model $C$ are made every day. It costs $Rs. 12000$ and $Rs. 15000$ each day to operate factory $I$ and $II,$ respectively. Find the number of days each factory should operate to minimize the operating costs and still meet the demand.