The Emerald Investment Group is considering investing in six projects. The expected net present value (NPV) and the required capital at the present time for each project are given in the table below. Project 1 2 3 4 5 Expected NPV ($) 6 6,000 8,000 3,000 5,000 7,000 4,000 Required Capital ($) 4,000 6,000 3,000 At present, a budget of $21,000 is available for investment. Emerald has specific requirements for the investment, as detailed in the Constraints section given below. 5,000 7,000 2,000

The Emerald Investment Group is considering investing in six projects. The expected net present value (NPV) and the required capital at the present time for each project are given in the table below. At present, a budget of $21,000 is available for investment. Emerald has specific requirements for the investment, as detailed in the Constraints section given below. What is the objective? Max Z=5,000X1+7,000X2+2,000X3+4,000X4+6,000X5+3,000X6 MinZ=6,000X1+8,000X2+3,000X3+5,000X4+7,000X5+4,000X6 MinZ=5,000X1+7,000X2+2,000X3+4,000X4+6,000X5+3,000X6 MinZ=X1+X2+X3+X4+X5+X6 MaxZ=6,000X1+8,000X2+3,000X3+5,000X4+7,000X5+4,000X6 MaxZ=X1+X2+X3+X4+X5+X6 Constraint on the budget. 5,000x1+7,000x2+2,000x3+4,000x4+6,000x5+3,000x621,0006,000x1+8,000x2+3,000x3+5,000x4+7,000x5+4,000x621,0005,000x1+7,000x2+2,000x3+4,000x4+6,000x5+3,000x6=21,0006,000x1+8,000x2+3,000x3+5,000x4+7,000x5+4,000x6=21,0005,000x1+7,000x2+2,000x3+4,000x4+6,000x5+3,000x621,0006,000x1+8,000x2+3,000x3+5,000x4+7,000x5+4,000x621,0005,000x1+7,000x2+2,000x3+4,000x4+6,000x5+3,000x621,000 If project 2 is selected, project 5 must be also selected. x2>x5x2x5x2+x51x2x5x2+x5=1x2+x51x2x6