Problem $5$: The Silver Star Bicycle Company will be manufacturing both men's and women's models for its

Easy$-$Pedal $10-$speed bicycles during the next two months. Management wants to develop a production schedule

indicating how many bicycles of each model should be produced in each month. Current demand forecasts call for

$150$ men's and $125$ women's models to be shipped during the first month and $200$ men's and $150$ women's models

to be shipped during the second month. Additional data are shown:

Last month the company used a total of $1000$ hours of labor. The company's labor relations policy will not allow

the combined total hours of labor $($manufacturing plus assembly$)$ to increase or decrease by more than $100$ hours

from month to month. In addition, the company charges monthly inventory at the rate of $2\%$ of the production

cost based on the inventory levels at the end of the month. The company would like to have at least $25$ units of

each model in inventory at the end of the two months.

Construct a model which will establish a production schedule that minimizes production and inventory costs

and satisfies the labor$-$smoothing, demand, and inventory requirements.