- The Tim Burr Company wants to best utilize the wood resources in one of its forest regions. Within this region, there is a saw mill and a plywood mill; thus, timber can be converted to lumber or plywood.
Producing a marketable mix of 1000 board feet of lumber products requires 1000 board feet of spruce and 3000 board feet of Douglas fir. Producing 1000 square feet of plywood requires 2000 board feet of spruce and 4000 board feet of Douglas fir. This region has available 32,000 board feet of spruce and 72,000 board feet of Douglas fir.
Sales commitments require that at least 4000 board feet of lumber and 12,000 square feet of plywood be produced during the planning period. The profit contributions are $40 per 1000 board feet of lumber products and $60 per 1000 square feet of plywood. The company is interested in maximizing profits. Provide a linear programming model formulation and solve for an optimal solution.
- Show & Sell can advertise its products on local radio and television (TV). The advertising budget islimited to $10,000 per month. Each minute of radio advertising costs $15 and each minute of TV commercials $300. Show & Sell likes to advertise on radio at least twice as much as on TV. In the meantime, it is not practical to use more than 400 minutes of radio advertising a month. From past experience, advertising on TV is estimated to be 25 times as effective as on radio. Show & Sell is interested in finding the optimum allocation of the budget to radio and TV advertising. Provide a linear programming model formulation only; you do not need to identify an optimal solution.
- Sunco processes oil into aviation fuel and heating oil. It costs $40 to purchase each 1000 barrels of oil, which is then distilled and yields 500 barrels of aviation fuel and 500 barrels of heating fuel. Output from the distillation may be sold directly or processed in the catalytic cracker. If sold after distillation without further processing, aviation fuel sells for $60 per 1000 barrels and heating oil sells for $40 per 1000 barrels. It takes 1 hour to process 1000 barrels of aviation fuel in the catalytic cracker, and these 1000 barrels can be sold for $130. It takes 45 minutes to process 1000 barrels of heating oil in the cracker and these 1000 barrels can be sold for $90. Each day, at most 20,000 barrels of oil can be purchased and 8 hours of cracker time are available. Sunco would like to maximize their profits. Provide a linear programming model formulation only; you do not need to identify an optimal solution.
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