Maximizing Profit Three kinds of wrapping paper are sold door-to-door by the local

Chapter 5, Problem 31

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Maximizing Profit Three kinds of wrapping paper are sold door-to-door by the local lacrosse team to raise funds for equipment. Birthday wrapping paper costs $3 a roll, takes (on average) 10 minutes to sell, and costs $0.50 to deliver to the customer. The holiday wrapping paper costs $5 a roll, takes 15 minutes to sell, and is left with the customer at the time of sale. The wedding wrapping paper costs $4 a roll, takes 12 minutes to sell, and costs $1 to deliver to the customer. During the fund-raiser, the team is allowed to sell up to $500 worth of the three types of wrapping paper and is allowed delivery expenses not to exceed $75. The team members times can be at most a total of 30 hours selling paper during the weeklong fund-raiser. Their profits are $1 for each roll of birthday paper and holiday paper they sell and $2 for each roll of wedding paper. What combination of sales of each type of paper will lead to a maximum profit for the team, and what is that profit? (a) Formulate a linear programming problem that models the problem given above. Be sure to identify all variables used. (b) Solve the linear programming problem. (c) Analyze the solution.