SuperMalls Inc. runs a chain of shopping malls across the Emirates. Recently, SuperMalls has purchased a 10,000 sq. ft building in Abu Dhabi, and the board is wondering how they should rent out the space in order to maximise profits. The following table presents the different types of shops that have shown an interest in renting space at the mall, together with the required space per shop, the minimum and maximum number of each shop type that SuperMalls wants to have at the mall, as well as the anticipated rent that SuperMalls receives from each such shop (in $1,000s). Shop type Space (sq ft) Minimum # Maximum # Rent Department 2,000 1 3 30 Accessories 500 0 3 8 Clothes 1,000 0 3 20 Book 750 1 3 15 Shoe 600 0 3 10

(a) How many shops of each type should SuperMalls have in the mall in order to maximise rent? Derive an Linear Program that solves the problem. You do not need to solve the problem!

(b) Construct a "good" solution to SuperMalls's problem. You can do this either via hand (in which case you should explain why this is a good solution) or by solving the Integer Program from part (a) with Excel (in which case you should submit the Excel sheet that you have used to solve the problem).