A production unit makes special type of metal chips by combining copper and brass. The standard weight of…
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
₹ 36
₹ 31
₹ 30
₹ 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 .
