There are two photo machines in the factory. Each of the machines can perform either of the two photo steps in the above process. The maximum allowed utilization of the photo machines is 80% (of total time). The factory works 24 hours per day, seven days per week. Assume line yield is 100%. (a) (4 points) Let xAt denote the amount of product A started into the process in week t. Let xBt denote the amount of product B started into the process in period t. Assume starts in each period are uniformly distributed over the period. Express the photo capacity constraint in week t. (b) (3 points) What starts of product A and product B need to be made in week 1 to ensure on- time delivery of the outstanding customer orders? Verify that such starts are capacity-feasible. (c) (5 points) The selling price of product A is $500 and the selling price of product B is $750. The incremental cost per start of each product is $50. Assuming the demand forecasts are accurate, what is the best production plan for week 1 starts