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 vitam…

Question

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 atleast 240 units of calcium, atleast 460 units of iron and atmost 300 units of cholesterol. The corner points of the feasible region are

Accepted Answer

Correct answer: A. (a) : Let the dietician uses x packets of food X and y packets of food Y. So, the mathematical formulation of the given problems is, 12x+3y 240 ⇒4x+y 80 (i) 4x+20y 460 ⇒x+5y 115 (ii) 6x+4y 300 ⇒3x+2y 150 (iii) x 0 ,y 0 The graph of the above equation is as follows: The shaded region is the feasible region. So, the required corner points are A (15 ,20 ) ,B (40 ,15 ), and C (2 ,72 ).

Solution

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