During the winter WeeMow Lawn Service contracts with customers for cutting lawns starting in the spring. WeeMow provides service to residential and commercial customers. The service has identified 50 possible residential customers and 15 potential commercial customers it has contacted. WeeMow services a customer once every 2 weeks during the growing season. A residential lawn on average takes 1.2 hours to cut, and a commercial property requires 5 hours to cut; the service’s available work time is 8 hours, 6 days per week. The profit for a residential lawn is $23, and the profit for a commercial property is $61. The service has established a weekly budget of $350 for management, gas, and other materials, plus equipment repair. A residential lawn averages $12 in management, gas, material, and repair costs, and a commercial property averages $20 in costs. WeeMow wants to know how many residential and commercial jobs it should contract for from among its potential customers in order to maximize profits.
a. Formulate a linear programming model for this problem.
b. Solve this model graphically.