A nutritionist dictates a diet containing at least 80 units of vitamin $A$ and 100 units of minerals. Two foods $F_1$ and $F_2$ are available. Food $F_1$ costs ₹4 per unit and $F_2$ costs ₹6 per unit. One unit of $F_1$ contains 3 units of vitamin $A$ and 4 units of minerals. One unit of $F_2$ contains 6 units of vitamin $A$ and 3 units of minerals. Formulate LPP and solve graphically to find minimum cost of diet.
Step-by-Step Solution
Constraints: $3x+6y \ge 80, 4x+3y \ge 100, x,y \ge 0$. Minimize $Z = 4x + 6y$. [1.5 Marks]
Intersection $(24, 4/3)$. [1.0 Mark]
Corner point table: $Z(24, 4/3) = 104, Z(80/3, 0) = 106.67, Z(0, 100/3) = 200$. [1.5 Marks]
Minimum cost $= ₹104$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Formulating mathematical diet model: 1.5 Marks
Evaluating intersection point: 1.0 Mark
Formulating corner point table: 1.5 Marks
Evaluating minimum cost $= ₹104$: 1.0 Mark
Correct Answer: