Ballmart is a retail store chain with 175 stores around the country. It is planning to undertake several sustainability (i.e., “green”) projects; it has been shown that sustainability projects can have a positive impact on cost (especially energy) savings and can generate positive media exposure. The projects being considered include installing solar panels at some or all of its stores, or installing small wind turbines; replacing some or all of Ballmart’s 165 trucks with more fuel-efficient hybrid trucks; waste reduction, including recycling; and the reduction of plastic bags in their stores. The costs for these projects, the resulting reduction in GHG emissions, the energy savings, and the annual costs savings are shown in the following table.

The “media public/relations score” in this table designates the importance of a particular project relative to the other projects in generating public awareness and publicity. For example, a score of “3” indicates that the solar power project will have the greatest public impact. However, Ballmart believes it will require a threshold number of projects to make an impact; specifically, a solar power installation for at least one store, wind power projects at three stores, at least ten new trucks, at least two waste recycling store projects, and at least six stores with plastic bag projects. $30 million has been budgeted for sustainable projects, and Ballmart wants to achieve GIG emission reductions of at least 250,000 metric tons per year; annual cost savings of at least $4 million; and, annual energy savings of at least 5 million kilowatt hours (kWh); while maximizing the public relations impact of its sustainability program.
a. Formulate and solve a linear programming model to determine how many projects of each type should be undertaken.
b. Reformulate and solve the model to maximize savings and not consider the media/public relations impact atall.

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Sustainable Projects Solar Shipping/ Waste Plastic Power Wind Power Vehicles RecyclingBags Media/ public relations 3 2 2 Cost $%2,600,000 950,000 38,000 365,000 175,000 GHG reductions (metric tons per year) Cost savings (S 220,000 125,000 26,000 75,000 45,000 17,500 8,600 1,700 900 savings (kWh) Units 400,000 150,000 34,000 1,200 55,000 75 75 165 75 75