HTM Realty has a storefront rental property in downtown Draperton, a small college town next to the Tech campus. The property encompasses four business spaces that open onto College Avenue. HTM has a long-term tenant in each space, and their leases are all running out at approximately the same time. HTM wants to significantly increase the rent for each space, and the current tenants have all indicated that they will stay on at a slightly increased rent but not at the rental price that HTM wants. HTM has shopped the spaces around and has gotten commitments from four new tenants at the higher rent. However, HTM realizes that there is a very high likelihood that the current tenants will remain in business and pay their rent for a new 3-year lease, whereas there is a much smaller likelihood that the new tenants will be able to stay in business and fulfill their lease payments. The following table shows the current and prospective new tenants for each space, their monthly payments for a 3-year lease, and the probability that each will remain in business:

HTM wants to lease each space to businesses that will maximize their expected lease payments. It also wants a likelihood that at least three of the businesses will stay in business. Formulate and solve an integer programming model for thisproblem.

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Current Lease New Lease Space TPayment Probability Tennt Payment Probability A Doughnut Shop 1,200 90Sub Shop B Jewelry Store C Music Store D Gift & Card Shop 1,100 90 Dress Shop 5 Restaurant 95 Tech Logo Ste 1,800 60 $2.400 50 1.200 70 40 800 1,000 2,000