A builder has to move at least 60 tonnes of sand. A truck carries 10 tonnes and a tractor carries 5 tonnes. At least 2 trucks and at least 4 tractors must be used. Hiring a truck costs Rs. 2000 and hiring a tractor costs Rs. 1200. The least cost of moving the sand is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs. 12800
Let x trucks and y tractors be hired. Then
Minimise \(Z = 2000x + 1200y\)
subject to
\(10x + 5y \ge 60\), that is \(2x + y \ge 12\) (sand)
\(x \ge 2\) (trucks)
\(y \ge 4\) (tractors)
The feasible region is unbounded. Its corner points:
\(x = 2\) and \(2x + y = 12\) meet at (2, 8)
\(y = 4\) and \(2x + y = 12\) meet at (4, 4)
Values of Z:
\(Z(2, 8) = 4000 + 9600 = 13600\)
\(Z(4, 4) = 8000 + 4800 = 12800\)
The half-plane \(2000x + 1200y \lt 12800\) has no point in common with the region, so the least cost is Rs. 12800 (4 trucks and 4 tractors).