A company is considering launching two new products that have large sales potential. Product 1 requires some of the production capacity in Plants 1 and 3, but none in Plant 2. Product 2 needs only Plants 2 and 3. The marketing division has concluded that the company could sell as much of either product as could be produced by these plants. However, because both products would be competing for the same production capacity in Plant 3, it is not clear which mix of the two products would be most profitable. Each product will be produced in batches of 20, so the production rate is defined as the number of batches produced per week. Any combination of production rates that satisfies these restrictions is permitted, including producing none of one product and as much as possible of the other. The number of hours of production time available per week in each plant for both products as well as the number of hours of production time required for each batch produced of each new product in each plant is given in the table below. The profit per batch of product 1 is $3000 and of product 2 is $2000. Answer the following