Consider an inventory problem with data shown in the table below.

	Period 1	Period 2	Period 3	Period 4
Demand	70	120	170	100
Production capacity	150	100	160	140
Unit production cost	$1	$1.1	$1.2	$1.3
Inventory cost	$.2 $.2 $.2

Formulate a cost-minimizing linear program. Clearly define all variables that you use. Assume that the opening inventory is zero & that no units of the product are required at the beginning of Period 5. Also assume that in each period, the production occurs before the demand. Solve the problem with LINDO/LINGO to answer the following questions:

(a) How many units should be produced in the four periods and what are the total costs?

(b) What are the inventory levels between the periods?

(c) What would happen if the production capacity in Period 1 would drop to 80?