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MHT CET202411 May 2024Evening ShiftMathematicsLinear ProgrammingActual

A production unit makes special type of metal chips by combining copper and brass. The standard weight of the chip must be at least 5 gms. The basic ingredients i.e. copper and brass cost ₹8 and ₹5 per gm. The durability considerations dictate that the metal chip must no contain more than 4 gms of brass and should contain minimum 2 gms of copper. Then the minimum cost of the metal chip satisfying the above conditions

Options

  1. A₹ 36
  2. B₹ 31
  3. C₹ 30
  4. D₹ 40

Correct answer

B. ₹ 31

Step-by-step solution

Let x and y denote the quantity of the basic ingredients of copper and brass respectively. cost, z=8 x+5 y Constraints are, aligned & x+y 5 & x 2 & y 4 & x 0, y 0 aligned Feasible region is as shown in the figure. Corner points of the feasible region are A (2,4), B(2,3) and C(5,0) z at A =36 , z at B =31 , z at C =40 Minimum cost is ₹ 31 .

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