Deep Train, Inc., a major logistics operator, has been contracted to transport finished

goods from three depots to retail outlets in four regions. The per unit shipping cost matrix

from each depot to each region is provided below.

To $->$

From $$

Region

$1$

Region

$2$

Region

$3$

Region

$4$

Available

supply

Depot $1141\mathrm{.}00228\mathrm{.}00260\mathrm{.}00122\mathrm{.}00450$

Depot $2250\mathrm{.}00116\mathrm{.}00263\mathrm{.}00278\mathrm{.}00700$

Depot $3182\mathrm{.}00132\mathrm{.}00120\mathrm{.}00185\mathrm{.}00500$

Required

Demand $450200300300$

$($a$)$ Formulate and solve the problem to determine the optimal shipping policy and the

optimum logistics cost$.$

$($b$)$ With a new expressway being built, the per unit transportation costs from Depot $3$ to

all regions reduces by $10\%,$ i$.$e$.,$ the new costs have now become $0\mathrm{.}9\backslash$times $3.$ Based on

the sensitivity report from part $($a$),$ is the optimal transportation policy likely to

change due to the reduction in costs?

Roadrunner, Inc. is a $$small$-$time$$ logistics company that wishes to make inroads into

retail deliveries. The CEO of this company makes the following two offers to Deep Train

Logistics, Inc.

Offer #$1$: Roadrunner offers to ship items to Region $1$ at a price of INR $200/$item$,$ i$.$e$.,$

Deep Train will have to pay Roadrunner a per unit cost of INR $200$ for every

item that they deliver to Region $1.$

Offer #$2$: Roadrunner will buy each item from Depot $3$ at its cost price and, pay an

additional fee of INR $70$ for each item purchased to Deep Train. Thus, if the cost

price of the item is INR $100,$ then Roadrunner will pay INR $170.($Roadrunner

uses these purchased items to be delivered to a different customer.$)$

$($c$)$ Is Offer #$1$ worthwhile? Why or why not? If yes, then how many items should

Roadrunner be allowed to deliver to Region $1?$

$($d$)$ Is Offer #$2$ worthwhile? Why or Why not? If yes, then how many items should be

$$sold$$ to Roadrunner from Depot $3?$

$($e$)$ Between the two offers, which one should Deep Train accept, if any? Why?