Only use Lingo or writing the objective function and constraints by hand.

Do not use Excel or other software plz.

7. Production Planning - Multi-period Planning A company has a demand for its product projected over the next 6 months as indicated in the table below. Month Demand 1 20 2 30 3 60 4 40 5 30 6 20 The demand must be met. There are currently 10 units in inventory. The remainder of the demand must be met by production. If the production in a month is greater than the demand, the excess is carried in inventory at a cost of $40 per unit per month. Employees make the product at the rate of 1 unit per month per worker. Fifteen are currently employed (at the beginning of the first month). Labor cost is $1000 per month per worker. The company can lay off workers at the beginning of any month at a cost of $600 each. The company can also hire new workers at the beginning of any month at a cost of $900 each. Each employee can work an extra 2 hours (in addition to an 8-hour day) at an overtime rate of 1.5 times the regular wage. The company has a budget of $50,000 per month for all expenses related to this problem. The problem is to find a policy for hiring and firing workers and the production level for the next 6 months. Set up this problem as a linear program. Model it using LINGO's modeling language and solve