Spencer Enterprises is attempting to choose among a series of new investment alternatives. The potential investment alternatives, the net present value of the future stream of returns, the capital requirements, and the available capital funds over the next three years are summarized as follows. Capital Requirements ($) Alternative Number Alternative Net Present Value ($) Year 1 Year 2 Year 3 1 Limited warehouse expansion 4,500 3,000 1,000 4,000 2 Extensive warehouse expansion 5,500 2,500 3,500 3,500 3 Test market new product 10,000 6,000 4,000 5,000 4 Advertising campaign 3,500 2,000 1,500 1,800 5 Basic research 8,500 5,000 1,000 4,000 6 Purchase new equipment 3,500 1,000 500 900 Capital funds available 10,500 7,000 8,750 i if investment alternative i is selected for i = 1, 2, 3, 4, 5, 6. (a) Develop an integer programming model for maximizing the net present value in $). Let x = 0 otherwise (Let x; = 5,6.) Max s.t. Year 1 Year 2 Year 3 According to this model, what is the maximum net present value (in $)? $ (b) Assume that only one of the warehouse expansion projects can be implemented. Modify your model from part (a). In addition to the constraints from part (a), what additional constraint should be added to the integer programming model? According to this model, what is the maximum net present value (in $)? $ (c) Suppose that if test marketing of the new product is carried out, the advertising campaign also must be conducted. Modify your formulation from part (b) to reflect this new situation. In addition to the constraints from part (a) and part (b), what additional constraint should be added to the integer programming model? According to this model, what is the maximum net present value (in $)? $ Spencer Enterprises is attempting to choose among a series of new investment alternatives. The potential investment alternatives, the net present value of the future stream of returns, the capital requirements, and the available capital funds over the next three years are summarized as follows. Capital Requirements ($) Alternative Number Alternative Net Present Value ($) Year 1 Year 2 Year 3 1 Limited warehouse expansion 4,500 3,000 1,000 4,000 2 Extensive warehouse expansion 5,500 2,500 3,500 3,500 3 Test market new product 10,000 6,000 4,000 5,000 4 Advertising campaign 3,500 2,000 1,500 1,800 5 Basic research 8,500 5,000 1,000 4,000 6 Purchase new equipment 3,500 1,000 500 900 Capital funds available 10,500 7,000 8,750 i if investment alternative i is selected for i = 1, 2, 3, 4, 5, 6. (a) Develop an integer programming model for maximizing the net present value in $). Let x = 0 otherwise (Let x; = 5,6.) Max s.t. Year 1 Year 2 Year 3 According to this model, what is the maximum net present value (in $)? $ (b) Assume that only one of the warehouse expansion projects can be implemented. Modify your model from part (a). In addition to the constraints from part (a), what additional constraint should be added to the integer programming model? According to this model, what is the maximum net present value (in $)? $ (c) Suppose that if test marketing of the new product is carried out, the advertising campaign also must be conducted. Modify your formulation from part (b) to reflect this new situation. In addition to the constraints from part (a) and part (b), what additional constraint should be added to the integer programming model? According to this model, what is the maximum net present value (in $)? $