Question $2$

$[20$ Marks A company has signed the following contract to supply customers A and B for the next $3$ months. June July $20$ Customer A Customer B $3020$ August $151020$ They can produce $40$ units per month at a cost of $100$ per unit on regular time and an additional $10$ units per month on overtime at a cost of $120$ per unit. They can store units at a cost of $10$ per unit per month. The contract allows the company to fall short on its supply commitment to customer A during the months of June and July, but this incurs a penalty cost of $5$ per unit; however, all shipments are to be completed by August. No shortages are allowed for customer B and his demands must be satisfied on the months specified. The company wishes to determine the optimal production schedule that will minimize the total cost of production, storage, and shortage. Formulate this as a transportation probelm by constructing the transportation table