Part A:$1.(25$ pts$)$ A food production and retail chain is considering several projects $($a$,$b$,$c$,$d$,$e$)$ that have varying capital requirements over the next $3$ years. The projects are possible plant expiation, possible warehouse expansion, possible additional of a transport unit, possible purchase of new machinery, and possible maintenance of machinery. The estimated net present value for each project, the investment requirements, and the available capital over the next $3$ years are shown below. All figures are in million dollars. Note that At least two projects must be selected. Machinery and Maintenance projects are dependent on each other $($If one of them is selected the other one must be selected as well$).$Which project$/$s company should choose to increase the present value? Formulate this problem.