all three questions please

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'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. Transportatio h Model Data Distribution Center Plant Houston San Jose Jacksonville Memphis Dallas 13.00 15.25 10.99 18.48 Atlanta 10.75 15.16 9.65 18.50 Demand 175 325 480 950 Answer the following question(s) using a linear optimization model. Capacity 1250 750 Answer the following question(s) using a linear optimization model. Which of the following is the constraint for total amount shipped from Atlanta? O X21 + X22 + X23+ X24 $ 750 X11 + X12 +X13 + X14 - X21 + X22 + X23 + X24 S 850 X21 + X22 + X23+ X24 1250 X11 +X12 + X13 + X14 S 1250 Answer the following question(s) using a linear optimization model. Which of the following is the objective function for cost minimization? minimize cost = 13X11 +15.25 X12 + 10.99X13 18.48 X14/10.75 X21 + 15.16 X22 * 9.65 X23* 18.5 X24 minimize cost = (13X11. 15.25 X 12 + 10,99X13 18.48X14 - 10.75 X21 + 15.16 X22 +9.65 X23 +18,5X24 X1,250 / 750) minimize cost - 13X11 15.25 X12 - 10.99 X13 + 18,48 X14 - 10.75 X21 + 15.16 X22 +9.65 X23 - 18.5X24 minimize cost - 13X11 - 15.25X12 + 10.99X13 + 18.48X14+ 10.75 X21 + 15.16 X22 - 9.65X23* 18.5X24 OOOO Answer the following question(s) using a linear optimization model. Which of the following is the constraint of nonnegativity for all values of land ? 13 X11 + 15.25X1210.99 X13 + 18.48X14/10.75 X21 + 15.16 X22 + 9.65 X23 + 18.5 X240 Xijs 0, for all i and (13X11 + 15.25X12 + 10.99 X13 18.48 X14 - 10.75 X21. 15.16 X22 +9.65X23 + 18.5 X24)(1.250/750) s 0 Xij 20, for all i and