A major expansion of the Brisbane airport14 will require moving substantial quantities of earth from 4 sites where it is surplus to 7 locations where it is needed. The following table shows the haul distances

(hundreds of meters) between points, as well as the quantity available (m3) at each surplus site.

Need Site Surplus Site Apron Term. Cargo Access Extension 26 28 20 26 Dry pond 12 14 26 10 Roads 10 12 20 4 Parking 18 20 2 16 Fire station 11 13 6 24 Industrial park 8 10 22 14 Perimeter road 20 22 18 21 Quantity available 660 301 271 99 Quantities needed are 247 cubic meters at the extension, 394 at the dry pond, 265 along roads, 105 in the parking area, 90 at the fire station, 85 in the industrial park, and 145 along the perimeter road.
The site engineer wishes to compute a minimum total distance times volume plan for accomplishing the required earth moving.

(a) Explain why appropriate decision variables for a model of this problem are 1i = 1,c, 4, j = 1,c, 72 xi, j!cubic meters moved from surplus i to need j

(b) Assign suitable symbolic names to the constants of the problem.

(c) Formulate an objective function to minimize total distance times volume movement.

(d) Formulate a system of 4 main constraints, assuring that the full available amount is moved from each surplus site.

(e) Formulate a system of 7 main constraints, assuring that the required amount is moved to each needing location.

(f) Complete your model with an appropriate system of variable-type constraints.
(g) Is your model best classified as an LP, an NLP, an ILP, or an INLP, and is it singleor multiobjective? Explain.
(h) Enter and solve your model with class optimization software.