A consultancy firm is preparing an office trip for its $400$ employees. The bus rental company has $2$ options for the buses that they can offer along with a maximum of $9$ drivers. The capacity and rental costs are shown below.

Determine the number of buses that the consultancy firm should book to minimise the total rental cost. Sketch the feasible region and show your steps.

$x = 4$ Large, $y = 5$ Medium

The correct answer is Option (3) → $x = 4$ Large, $y = 5$ Medium ##

Let the number of large buses be $x$ and medium buses be $y$. We write the LPP as:

Minimise $Z = 3000x + 2000y$

Subject to the constraints:

$\begin{aligned} 50x + 40y \ge 400 \\ x + y \le 9 \\ x \ge 0, y \ge 0 \end{aligned}$

The objective function value at the $3$ corners of the feasible region is:

Conclude that the consultancy firm should book $4$ large buses and $5$ medium buses to minimize cost.