A furniture company manufactures tables and chairs. A table requires 45 board-feet of wood, and a chair requires 20 board-feet of wood. Wood can be purchased at a cost of $1.90 per board-foot, and 25,000 board-feet of wood are available for purchase. It takes 2.5 hours of skilled labor to manufacture an unfinished table or an unfinished chair. Then 3 more hours of skilled labor will turn an unfinished table into a finished table, and 1.5 more hours of skilled labor will turn an unfinished chair into a finished chair. A total of 4500 hours of skilled labor is available (and have already been paid for). All furniture produced can be sold at the following unit prices: an unfinished table, $180; a finished table, $330; an unfinished chair, $130; and a finished chair, $200. a. Determine how to maximize the company’s profit from manufacturing tables and chairs. b. Use a two-way SolverTable to see how the numbers of unfinished products (both chairs and tables) sold depend on the selling prices of these unfinished products. Of course, neither unfinished selling price should be as large as the corresponding finished selling price.
A furniture company manufactures tables and chairs. A table requires 45 board-feet of wood, and a chair requires 20 board-feet of wood. Wood can be purchased at a cost of $1.90 per board-foot, and 25,000 board-feet of wood are available for purchase. It takes 2.5 hours of skilled labor to manufacture an unfinished table or an unfinished chair. Then 3 more hours of skilled labor will turn an unfinished table into a finished table, and 1.5 more hours of skilled labor will turn an unfinished chair into a finished chair. A total of 4500 hours of skilled labor is available (and have already been paid for). All furniture produced can be sold at the following unit prices: an unfinished table, $180; a finished table, $330; an unfinished chair, $130; and a finished chair, $200.
a. Determine how to maximize the company’s profit from manufacturing tables and chairs.
b. Use a two-way SolverTable to see how the numbers of unfinished products (both chairs and tables) sold depend on the selling prices of these unfinished products. Of course, neither unfinished selling price should be as large as the corresponding finished selling price.
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