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KCET2022MathematicsLinear Programming

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, atleast 460 units of iron

Options

  1. A(2,72),(40,15),(15,20)
  2. B(2,72),(15,20),(0,23)
  3. C(0,23),(40,15),(2,72)
  4. D(2,72),(40,15),(115,0)

Correct answer

A. (2,72),(40,15),(15,20)

Step-by-step solution

Let x and y be the number of packets of food X and Y array ll & x 0, y 0 12 x+3 y 240 & 4 x+y 80 & 4 x+20 y 460 & x+5 y 115 & 6 x+4 y 300 & 3 x+2 y 150 & x 0, y 0 & 4 x+y 80 array Intersection points of the lines are shown in the graph we can see that corner point of the feasible region A, B and C are (2,72),(40,15),(15,20) .

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