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MHT CET2011MathematicsLinear Programming

A diet of a sick person must contain atleast 4000 unit of vitamins, 50 unit of proteins and 1400 calories. Two foods A and B are available at cost of ₹ 4 and ₹ 3 per unit respectively. If one unit of A contains 200 unit of vitamins, 1 unit of protein and 40 calories, while one unit of food B contains 100 unit of vitamins, 2 unit of protein and 40 calories. Formulate the problem, so that the diet be cheapest.

Options

  1. A200 x+100 y 4000, x+2 y 5040 x+40 y 1400, x 0 and y 0O . F z=4 x+3 y
  2. B400 x+200 y 100, x+2 y 5040 x+40 y 1400, x 0 and y 0 O. F z=4 x+3 y
  3. C100 x+200 y 4000, x+2 y 50 , 40 x+40 y 1400, x 0 and y 0 O. F z=4 x+3 y
  4. DNone of the above

Correct answer

A. 200 x+100 y 4000, x+2 y 5040 x+40 y 1400, x 0 and y 0O . F z=4 x+3 y

Step-by-step solution

array l|c|c|c|c array c Nutrients Food array & array c Vitamins (unit) array & array c Proteins (unit) array & array c Colories (unit) array & array c Availabil ity (per unit) array A & 200 & 1 & 40 & 4 pes B & 100 & 2 & 40 & 3 pes Requirement & 4000 & 50 & 1400 & array Let z be the profit function and x and y denote the productivity of food A and B respectively. Then array c 200 x+100 y 4000 x+2 y 50 40 x+40 1400 O.F z=4 x+3 y, x 0 and y 0 array

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