Introduction to Management Science 12th Edition by Bernard Taylor

تمرين 63

Solve the linear programming model for WeeMow Lawn Service in Problem using the computer.
a. Which resources constrain how many jobs the service can contract for
b. If WeeMow could increase its weekly budget by $50 per week, or increase its workday to 9 hours, which would be more profitable
c. The solution to this problem should logically be integer, that is, whole jobs; however, the optimal solution is not integer. How would you suggest that WeeMow address this discrepancy Do you think there is a way to handle this problem with the computer program you are using to solve this problem
Problem
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.