$A$ wholesale merchant wants to start a cereal business with $Rs \ 24000$. Wheat costs $Rs \ 400$ per quintal and rice costs $Rs \ 600$ per quintal. He has a storage capacity of $200$ quintals of cereal. He earns a profit of $Rs \ 25$ per quintal on wheat and $Rs \ 40$ per quintal on rice. If he stores $x$ quintals of rice and $y$ quintals of wheat,then for maximum profit,the objective function is:
- A$25x + 40y$
- B$40x + 25y$
- C$400x + 600y$
- D$\frac{400}{40}x + \frac{600}{25}y$
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$A$ 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 correct constraints for the given feasible region are:
Cake-$A$ requires $200\, g$ of flour and $25\, g$ of fat. Cake-$B$ requires $100\, g$ of flour and $50\, g$ of fat. Find the maximum number of cakes which can be made from $5\, kg$ of flour and $1\, kg$ of fat. The mathematical form of this $LPP$ is $.....$
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View Solution$A$ dietician wishes to mix together two kinds of food $X$ and $Y$ in such a way that the mixture contains at least $10$ units of vitamin $A$,$12$ units of vitamin $B$,and $8$ units of vitamin $C$. The vitamin contents of one $kg$ of food are given below:
Food Vitamin $A$ Vitamin $B$ Vitamin $C$ $X$ $1$ $2$ $3$ $Y$ $2$ $2$ $1$
One $kg$ of food $X$ costs $Rs. 16$ and one $kg$ of food $Y$ costs $Rs. 20$. Find the least cost of the mixture which will produce the required diet?
| Food | Vitamin $A$ | Vitamin $B$ | Vitamin $C$ |
| $X$ | $1$ | $2$ | $3$ |
| $Y$ | $2$ | $2$ | $1$ |
One $kg$ of food $X$ costs $Rs. 16$ and one $kg$ of food $Y$ costs $Rs. 20$. Find the least cost of the mixture which will produce the required diet?
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View SolutionThe maximum value of $z=4x+2y$,subject to the constraints $3x+4y \geqslant 12$,$x+y \leqslant 5$,$x, y \geqslant 0$ is
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