The local public utilities commission has been charged with inspecting and reporting utility problems in the area. They have three electrical inspectors and two gas inspectors, each available for 40 hours , to analyze structures in their respective areas of expertise. In addition the commission has $10,000 for up to 10 hours ( at $100 per hour) of expert consultant support to inspect insulation. Any facility inspected requires all three types of inspections ( naturally one of each per facility).
These experts will inspect private homes business ( office buildings) and industrial plants in the area. The goal is to inspect as many structure as possible however the minimum requirements are to inspect at least eight office buildings and eight industrial plants and to make sure that at least 60% of the inspection are of private homes.
Once the total number of each type of structure to be inspected has been determined, the actual inspection will be done by choosing a random sample from those that are served by the commission. The commission will plan using the following approximate inspection hours for each type of inspection:
Formulate a linear program to help the commission determine how many of each structure they should inspect. You do not need to implement this model in excel. You do not need to solve the problem and report a solution. You may wish to do so as a means to verify your formulation and to check your work. I will not consider a working excel model as a substitute for the accurate mathematical formulation.