# A real estate developer is planning to build an office complex. Currently, there are three office...

## Question:

A real estate developer is planning to build an office complex. Currently, there are three office sizes under consideration: small, medium, and large. Small offices can be rented for $600 per month, medium offices can be rented for$750 per month, and large offices can be rented for \$1000 per month. Each small office requires 600 square feet, each medium office requires 800 square feet, and each large office requires 1000 square feet. The current plot of land available to the developer is 100,000 square feet. The developer wants to ensure that the office complex has at least 3 units of each office size.

Write the linear programming formulation to determine how many of each office size to build in order to maximize total revenue.

## Linear Programming

Linear programming is done just like any other optimization problem where you maximize (or minimize) your objective function given a constraint but instead of having just one constraint we may have multiple ones.

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Let {eq}s, m, l {/eq} be small, medium, and large offices respectively.

{eq}\max\limits_{s,m,l} \thinspace 600s+750m+1000l \space s.t. \space...