2-18. A manufacturer has contracted to produce 2,000 units of a particular product over the next eight months. The manufacturer has estimated that it costs her $1 Deliveries are scheduled as follows: to store one unit of product for one month. She has a warehouse capacity of 300 units. The manufacturer can produce any number of units Month in a given month, since the units can be produced mostly with part-time labor, which can be easily January 100 obtained. However, there are costs of training new February 200 personnel and costs associated with laying off personnel March 300 who have been hired. The manufacturer has estimated April 400 that it costs approximately 75 cents per unit to increase May 100 the production level from one month to the next (e.g., if June 100 July production in January is 200 and is increased to 300 in 500 August 300 February, the cost is $75 for training the additional people required to produce at the 300-unit level). Total 2,000 Similarly, it costs 50 cents per unit to reduce production from one month to the next. (At the end of eight months, all employees will be laid off, with the corresponding production-reduction costs.) Assume the production level before January is zero. a. Formulate the above as a linear programming problem. b. Suppose there is a limit on production of 300 units per month. Formulate the linear programming problem with this additional constraint