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The St. Joseph Public Utilities Commission has been charged with inspecting and reporting utility problems that have resulted from recent floods in the area. Concerns have been raised about the damage done to electrical wiring, gas lines, and insulation. The Commission has one week to carry out its inspections. It has been assigned 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 allocated $10,000 for up to 100 hours (at $100 per hour) of consulting time from Weathertight Insulation, a local expert in home and industrial insulation. These experts are assigned to inspect private homes, businesses (office complexes), and industrial plants in the area. The goal is to thoroughly inspect as many structures as possible during the allotted time in order to gather the requisite information. 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 inspections are of private homes. Once the total number of each type of structure to be inspected has been determined, the actual inspections will be done by choosing a random sample from those that are served by the St. Joseph Public Utility Commission. The Commission has mandated the following approximate inspection hours for each type of inspection: A team of management science consultants has been hired to suggest how many homes, office buildings, and plants should be inspected. The following is a brief summary of the problem faced by the St. Joseph Public Utilities Commission. - St. Joseph must determine the number of homes, office complexes, and plants to be inspected. - It wishes to maximize the total number of structures inspected. - At least eight offices and eight plants are to be inspected. - At least 60% of the inspections should involve private homes. - At most, 120 hours (340) can be allocated for electrical inspections, 80 hours (240) for gas inspections, and 100 consulting hours for insulation inspection. Determine the maximum number of structures that can be inspected, subject to the constraints