Consider an identical scenario to the transportation problem discussed in class $($Example

$3-3$ on pages $92-93),$ except that transportation costs per unit along the links are given by

$($in dollars$/$unit$)$

Facility p$1$ p$2$ c$1$ c$2$ c$3$

w$134345$

w$252212$

Solve $($that is$,$ determine the product flows on each of the links and also the total cost$)$

each of the following scenarios independently:

$($a$)$ Formulate the LP $($linear program$)$ and solve it$,$ i$.$e$.,$ determine the optimal product

flows on each of the links and also the minimum total cost.

$($b$)$ Suppose you have the option of paying a fixed cost of C in order to hire a fleet of

more fuel$-$efficient trucks. The fuel$-$efficient trucks will reduce all of the per unit

transportation costs given in the table above by $$1.$ Solve the resulting fuel$-$efficient

LP and determine the range of C for which you will prefer to hire the more fuel$-$efficient

trucks.

$($c$)$ Suppose you considering adding capacity to plant $2,$ in order to remove the capacity

constraint. How much money could you save on the transportation cost if you were

to do this?