Question

Q4. A post office is planning to build mail boxes along a wall in the mail room that is 1.8 metres high and 12 metres wide. The boxes come in two sizes: large boxes are 25cm wide and 15cm high; small boxes are 12cm wide and 10cm high. To simplify the design of the space, it has been decided that columns will contain exclusively large boxes or exclusively small boxes (i.e, no column will contain a mixture of large and small boxes). Post office officials have determined that at least half the available space should contain large boxes.
Determine the design in order to have the maximum number of boxes. Just build the LP program – not need to figure out the optimal values.

Answer 1

Variable definition:

X= Number of columns of large boxes

Y= Number of columns of small boxes

For reference:

1 meter = 100 cm

Objective function:

Each column of large boxes will have 12 boxes (180/15=12).

Each column of small boxes will have 18 boxes (180/10=18).

To maximize the number of boxes

Maximize Z = 12*X + 18*Y

Constraints:

25*X + 12*Y <=1200 (Total width of boxes cannot be greater than mailroom width [12 meters])

X, Y>=0 (Non-negativity constraint as number of columns cannot be negative)

Also,

Space occupied by large boxes >= 50%* space available

X*25*15*12 >=0.5*(180*1200)

X>=24