Formulate as an ILP ONLY The figure represents a grid on which electric power is generated and distributed. Each node is a demand point and also a potential location for a power generator. The numbers in parentheses indicate power demands in megawatts (MW). Assume that the grid is in the xy-plane, where x, y = 0, 1, 2, 3. (17) (5) (3) (10) (8) (10) (10) (15) (10) (12) (20) (18) (12) (8) (12) (5) Power will be supplied by generators constructed at the nodes. The maximum size of a plant in terms of power output is 100 MW. The cost of a plant in scaled terms consists of a fixed charge of $100 plus a variable cost of $2 per megawatt. In the model, all costs are expressed as lifetime figures, so no adjustment need be made to account for the time value of money or the differences between oper- ating and investment costs. Power is transmitted along the lines that connect the nodes (all parallel to the grid axes). The cost of transmission is $1.5 per megawatt per mile. Note that the distance between adjacent nodes is 1 mile. Power may flow in either direction along a line and is delivered to the cus tomers at the nodes. Excess power arriving at a node may be transshipped along the lines to other nodes. The problem is to select the nodes at which generators should be built as well as to determine the sizes of the generators. The solution must satisfy the following environmental restrictions. No two generators may be less than 1.5 miles apart No more that two generators may be built on any coordinate line. For instance, of the four loca tions on the vertical axis x = 1, at most two can be used If a generator is built at location (3, 3), one must also be built at location (0, 0) Set up and solve a mathematical programming model for this problem