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 is

• A

  ₹ 36
• Correct answer
  B

  ₹ 31
• C

  ₹ 30
• D

  ₹ 40

Solution

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

Hence, the correct answer is option: 'B'.