Formulate a linear programming model for this problem. (When you are asked to formulate a linear programming model, you need to write down explicitly the decision variable definition, objective function and constraints.)

Use the graphical method to solve this problem (including, clearly showing the feasible region on a graph, labeling the extreme points, and identifying the optimal solution and the corresponding optimal objective function value).

A transit-mix company markets2 concrete mixes, A and B. The company can produce up to 14 truckloads per hour of mix A or up to 7 loads per hour of mix B. The available trucks can haul up to 7 loads per hour of mix A and up to 12 loads per hour of mix B, due to the differences in delivery distances. The loading facility can handlc not more than 8 truckloads per hour regardlcss of the mix. The company anticipates a profit of $5 per load on mix A and S10 per load on mix B. What number of loads per hour of each mix should the company produce? A transit-mix company markets2 concrete mixes, A and B. The company can produce up to 14 truckloads per hour of mix A or up to 7 loads per hour of mix B. The available trucks can haul up to 7 loads per hour of mix A and up to 12 loads per hour of mix B, due to the differences in delivery distances. The loading facility can handlc not more than 8 truckloads per hour regardlcss of the mix. The company anticipates a profit of $5 per load on mix A and S10 per load on mix B. What number of loads per hour of each mix should the company produce