$4$

$($c$)[2]$ If we can add $10$ more units of supply, which distribution center should these $10$ units be added to$?$ What is the new total shipping cost? Explain. Answer this question by reading from the sensitivity report without resolving the linear program.

$($d$)[2]$ In your optimal solution, how many units are being shipped from Atlanta to Dallas? If zero, how much should the shipping cost $($currently $$27)$ decrease for the optimal solution to ship nonzero units from Atlanta to Dallas? If not zero, how will the optimal solution and the optimal solution value change if the cost is increased to $$28?$ Explain. Answer this question by reading from the sensitivity report without resolving the linear program.

$($e$)[2]$ In your optimal solution, how many units are being shipped from Topeka to Riverside? If zero, how much should the shipping cost $($currently $$35)$ decrease for the optimal solution to ship nonzero units from Topeka to Riverside? If not zero, how will the optimal solution and the optimal solution value change if the cost is increased to $$36?$ Explain. Answer this question by reading from the sensitivity report without resolving the linear program.

$3$

$2.[14]$ ABC Trucking has three distribution centers $($DCs$)$ located in Dallas, Jersey City, and Riverside that transport product each week to warehouses located in five cities: Seattle, Topeka, Minneapolis, Atlanta, and Boston. Each DC has an upper limit on the number of units of product that it can ship each week and each warehouse has a requirement for the volume of product needed. These values and the per unit shipping costs for all DC$-$warehouse pairs are provided in the accompanying Excel workbook.

$\backslash$table$[[,$DISTRIBUTION CENTERS,$],[$WAREHOUSES$,$Dallas,Jersey City,Riverside,REQUIREMENT$],[$Seattle$,$$$30,$$$50,$$$37,50],[$Topeka$,$$$13,$$$40,$$$35,60],[$Minneapolis$,$$$36,$$$41,$$$50,40],[$Atlanta$,$$$27,$$$35,$$$48,65],[$Boston$,$$$40,$$$10,$$$60,55],[$SUPPLY LIMIT,$100,100,100,]]$

ABC seeks a feasible shipping plan that minimizes the total shipping cost.

$($a$)[4]$ Formulate this transportation problem as a linear program. Clearly define your decision variables, objective function, and constraints $($Hint: Let $x_{IK}$ be the amount shipped from DC$,$ for $I=D,J,R,$ to the warehouse $K,$ for $K=S,T,M,A,B.$ Note the letters correspond to the first letter of the cities above. For example, $x_{DS}$ is the amount shipped from Dallas to Seattle$).$

$($b$)[4]($Excel$)$ Solve this linear program in the Excel workbook. What is the minimum total shipping cost? Write down the answer here; save the answer report and the sensitivity report in Excel.