MS $3053-$ Problem Set #$4$

Due Date: March $6,2024$

#$1$

A grocery store chain has $$34$ million that it wishes to devote to expansion into a new territory. The company can construct two types of stores, standard $($which sells food products and basic household items$)$ and deluxe $($which additionally sells items such as home goods and clothing$).$ Construction costs are $$2\mathrm{.}6$ million per standard store and $$4\mathrm{.}1$ million per deluxe store. There is no limit to the number of standard stores that can be constructed; however, due to variour non$-$compete clauses, no more than four deluxe stores may be constructed in the territory. The company has hired a territorial manager for these properties who can devote up to $36$ hours per week for field visits. Including travel time, each standard store will require $3\mathrm{.}75$ hours per week of field visitation time; each deluxe store will only require only $2\mathrm{.}25$ hours per week of field visitation time, as they will have larger on$-$site management teams. The weekly net revenue is projected to be $$81,000$ per standard store and $$132,000$ per deluxe store. Develop an integer programming model to determine the optimal number of each type of store to build, with the goal of maximizing total weekly revenue. Provide all constraints in standard form. You do not need to solve the LP$.$

#$2$