$[14]$ 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.

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.