Quality Ingredients Inc. specializes in producing gourmet spice blends, utilizing premium herbs, spices, and botanicals in three separate facilities. The monthly inventory for these inputs changes each month, as shown in Table 1. The company has the option to store purchased ingredients in inventory for future use. It is assumed that there are no initial inventories. Table 2 presents the input requirements and sales prices for each blend. Furthermore, there are maximum restrictions on the flavor, aroma, and color content for each blend, based on customer preferences (Table 3). The flavor, aroma, and color values for the input ingredients are provided in Table 4. Each facility has a dedicated production capacity for each blend, as shown in Table 5. Table 2 Table 3 Table 4 Table 5 Decision Variables: Xi,f,t : Amount of Blend i produced in Facility f in Month t. Yj,t : Amount of Product j in the inventory at the beginning of the Month t. zi,j,t : Amount of Product j used for Blend i in Month t. If you formulate the linear programming model that satisfies the requirements and maximizes profits using the decision variables above, how should you formulate the objective function? Correct: 6 pts Incorrect: 6pts Correct: 6 pts Incorrect: -6 pts a. a.120(X1,1,1+X1,2,1+X1,3,1+X1,1,2+X1,2,2+X1,3,2++X1,3,6)+144(X2,1,1+X2,2,1+X2,3,1+X2,1,2+X2,2,2+X2,3,2++X2,3,6)+120(X3,1,1+X3,2,1+X1,3,1+X3,1,2+X3,2,2+X3,3,2++X3,3,6) b. 120(X1,1,1+X2,1,1+X3,1,1+X1,1,2+X2,1,2+X3,1,2++X3,1,6)+144(X1,2,1+X2,2,1+X3,2,1+X1,2,2+X2,2,2+X3,2,2++X3,2,6)+120(X1,3,1+X2,3,1+X3,3,1+X1,3,2+X2,3,2+X3,3,2++X3,3,6) c. 120(X1,1,1+X2,1,1+X3,1,1+X1,1,2+X2,1,2+X3,1,2++X3,1,6)(Y1,1+Y1,2++Y16)+144(X1,2,1+X2,2,1+X3,2,1+X1,2,2+X2,2,2+X3,2,2++X3,2,6)(Y2,1+Y2,2++Y26)+120(X1,3,1+X2,3,1+X3,3,1+X1,3,2+X2,3,2+X3,3,2++X3,3,6)(Y3,1+Y3,2++Y36) d. 120(X1,1,1+X1,2,1+X1,3,1+X1,1,2+X1,2,2+X1,3,2++X1,3,6)(Y1,1+Y1,2++Y16)+144(X2,1,1+X2,2,1+X2,3,1+X2,1,2+X2,2,2+X2,3,2++X2,3,6)(Y2,1+Y2,2++Y26)+120(X3,1,1+X3,2,1+X1,3,1+X3,1,2+X3,2,2+X3,3,2++X3,3,6)(Y3,1+Y3,2++Y36) e. Z1,1,t+Z1,2,t+Z1,3,t+Z2,1,t+Z2,2,t+Z2,3,t+Z3,1,t+Z3,2,t+Z3,3,t=X1,1,t+X1,2,t+X1,3,t+X2,1,t+X2,2,t+X2,3,t+X3,1,t+X3,2,t+X3,3,tt in month