(1 point) A cargo plane has three compartments for loading cargo: "front" 1, "center" 2, and "back" 3. the front has a maximum capacity of 12 tons and 7000 cubic feet; the center has a maximum capacity of 18 tons and 9000 cubic feet; the back has a maximum capacity of 10 tons and 5000 cubic feet whenever the plane is loaded they have to balance the load in the same proportions as indicated in the total capacity (i.e. in the center hold would be 18/40 of the total load. A client has four types of cargo, simply denoted 1,2,3,4 ; in the amounts 20, 16, 25, and 13 tons respectively. Each cargo 1 is 500 cubic ft / ton, cargo 2 is 700 cubic ft/ton, cargo 3 is 600 cubic ft/ton, and cargo 4 is 400 cubic ft/ton. The client is willing to pay (dollars per ton) 320, 400, 360, and 290 for cargo 1, 2, 3, and 4 respectively. Formulate and then solve to find the maximum profit for a single flight. The maximum total profit subject to the conditions is Check the values of the decision variables in your solution and determine the number of tons of cargo 3 that has been loaded in the front hold. Now pick a number k between 1 and 5 that is different from your solution and impose the additional constraint that the number of tons of cargo 3 in the front hold equals k. Find the new optimal solution. What is your new solution for max profit? Does the original problem have alternate solutions? ("Yes" or "No")