Use the table below to answer the following question$($s$).$

The Riviera Transport Company $($RTC$)$ produces car accessories at two plants: Dallas and Atlanta. They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis. The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands. RTC$\text{'}$s supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost, not exceed available capacity, and meet customer demand.

Assume Xij $=$ amount shipped from plant i to distribution center j$,$ where i $=1$ represents Dallas, i $=2$ represents Atlanta, j $=1$ represents Houston, and so on$.$

Transportation Model $$

$$

Data $$

$$ Distribution Center $$

Plant Houston San Jose Jacksonville Memphis Capacity

Dallas $13\mathrm{.}0015\mathrm{.}2510\mathrm{.}9918\mathrm{.}481250$

Atlanta $10\mathrm{.}7515\mathrm{.}169\mathrm{.}6518\mathrm{.}50750$

Demand $175325480950$

Answer the following question$($s$)$ using a linear optimization model.

According to the Sensitivity Report, which of the following is true if the capacity at Atlanta is increased by $230$ units?

Question $21$ options:

the total cost per unit will reduce by $$\mathrm{.}09$ to Memphis

the shadow price at Atlanta will increase to $$0\mathrm{.}09$

the total cost at Atlanta increases by $$9$

the total cost can be reduced by $$\mathrm{.}09$ per unit