The marketing manager for Glissen Paint is working on the weekly sales and marketing plan for the firm’s industrial and contractor sales staff. Glissen’s sales representatives contact two types of customers: existing customers and new customers. Each contact with an existing customer normally takes 3 hours of the salesperson’s time (including travel time) and results in an average sale of $425. Contacts with new customers generally take a bit longer, on average 4 hours, and result in an average sale of $350. The company’s salespeople are required to work 40 hours a week, but often work more to achieve their sales quotas (on which their bonuses are based). The company has a policy limiting the number of hours a salesperson can work to 50 hours per week. The sales manager wants to set customer contact quotas for the salespeople that will achieve the following goals (listed in order of importance):

Goal 1: Each salesperson should achieve an average weekly sales level of $6,000.

Goal 2: Each salesperson should contact at least 10 existing customers per week.

Goal 3: Each salesperson should contact at least 5 new customers per week.

Goal 4: Each salesperson should limit overtime to no more than 5 hours per week.

a. Formulate this problem as a GP with an objective of minimizing the sum of the weighted undesirable percentage deviation from the goals.

b. Implement your model in a spreadsheet and solve it assuming equal weights on each goal. What solution do you obtain?