A company produces two kinds of products (A and B) in a single machine. The machine operates for 20h every day. The production of each item A consumes 3h of the machine time while the production of each item B consumes 5h of the machine time. You want to plan the operations for the next 3 days. The demand of each product i = {A, B} for each day t = {1,2,3} is given by dit. You currently have 1 unit of product A in inventory and 2 units of product B in inventory. The production cost of each product varies according to the day due to changes in electricity price. The cost to produce item i = {A, B} on day t = {1,2,3} is given by cit. You can assume that a product left unfinished on a day can be completed on the following day. a) Formulate a linear programming problem that minimises production cost while meeting the demand. Clearly define the variables you use and briefly explain the meaning of each constraint. b) What would change in your model if there is a storage cost of hit for each product of type i = {A, B} in inventory at the end of day t = {1,2,3}? c) What would change in your model if the products can not be left unfinished on any given day?