EX3.Resource Allocation A furniture manufacturer has plants in Austin, TX and Huston, TX. For a popular dining table and chair set that they sell for $1,200, they face the following logistics problem: Austin, TX Capacity = 2,400 New York: Demand = 1,500 Atlanta: Demand = 1,000 Chicago: Demand = 1,250 Huston, TX Capacity = 3,500 Cincinnati: Demand = 750 Detroit: Demand = 1,000 To determine how much to ship from each plant to each market, we need to know the per-uni transportation costs. For example, the per-unit transportation cost from Austin to Chicago is $225. CHI CINC DET $175 $175 NY ATL $150 $100 $225 $150 $200 $100 $100 $100 Austin Huston Note that, given the variable production costs of $500 (Austin) and $550 (Lansing), the total per-unit cost of supplying the markets is: e CHI CINC DET $650 $600 $725 $675 $675 $700 $750 $650 $650 s650 NY ATL Austin Huston For example, the total per-unit transportation cost from Austin to Chicago is $725 (=$500+S225). Your tasks: (a) Write the decision variables, objective function, and constraints. (b) Solve the problem using an Excel solver: what is your optimal solution? e ottttt