Question

c) The Star hotel was burned down in a fire and the manager decided to accommodate the

guests in 4–person and 8-person tents. The tents were to be hired at a cost of Kshs 1,500 and

Kshs 4,500 per night respectively, the space available could accommodate at most 13 tents

and the manager had to cope with at least 64 guests.

Required

Formulate this as a linear programming model that could be used to determine the number

of tents of each type that could pull up in order to minimize the overall cost.

Answer 1

Solution:

Let the number of 4-person tents and 9-person tents be $x,\ y$ respectively.

Constraints:

$x+y\le13 \\ 4x+8y\ge64 \\ x,y\ge0$

Objective function: Minimize $Z=1500x+4500y$

This is the required LPP.