Formulate the problem as a linear program (define the decisions variables clearly, write the objective function and constraints in terms of those variables.) PROTRAC produces the largest member of its earth-moving equipment line (the E-9) and the largest member of its forestry equipment line (the F-9) with essentially the same equipment. Demand for these items is very high at this time, and management believes it is possible to sell as many of both as the firm can produce. The profit is $5000 for each E-9 sold, and $4000 for each F-9 sold. In the production planning for the next 2 weeks, management knows it is necessary to produce a total of at least five E-9s and F-9s in order to meet previous commitments. Management Science (Mgmt 101 ) Winter 2016 Each of these products requires processing two departments A and B. Each E-9 requires 10 hours of work in department A and 20 hours in department B, whereas each F-9 requires 15 hours of work in department A and 10 hours in department B. Over the next 2 weeks, these departments have 150 and 140 hours of available time, respectively. Additionally, each finished E-9 unit needs to go through 30 hours of testing and each F-9 requires 10 hours of testing. In order to honor the labor contract, the total labor hours used in testing finished products cannot fall more than 10% below the agreed goal of 150 hours. (This is independent of the processing requirements in departments A and B.) Finally, in order to maintain the current market position, management feels that it is necessary to build at least one F-9 for every three E-9s produced. How many of each product should PROTRAC produce in the next 2 weeks to maximize profit?