$A$ dietician has to develop a special diet using two foods $X$ and $Y$. Each packet (containing $30 \ g$) of food $X$ contains $12$ units of calcium,$4$ units of iron,$6$ units of cholesterol and $6$ units of vitamin $A$. Each packet of the same quantity of food $Y$ contains $3$ units of calcium,$20$ units of iron,$4$ units of cholesterol and $3$ units of vitamin $A$. The diet requires at least $240$ units of calcium,at least $460$ units of iron and at most $300$ units of cholesterol. The corner points of the feasible region are:
- A$(2,72), (40,15), (15,20)$
- B$(2,72), (15,20), (0,23)$
- C$(0,23), (40,15), (2,72)$
- D$(2,72), (40,15), (115,0)$
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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:
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| 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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The feasible region of the $L$.$P$.$P$. (Linear Programming Problem) to maximize $z = 70x + 50y$ subject to the constraints $8x + 5y \leq 60$,$4x + 5y \leq 40$ and $x \geq 0, y \geq 0$ is:
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