The Zrek Bicycle Company will be manufacturing both men's and women's models for their Easy-Pedal 10-speed bicycles during the next 2 months. The company would like 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 below.

Model	Costs ($)	Labor Requirements (hrs)	Current Inventory
Manufacturing	Assembly
Mens	150.00	2.1	1.5	15
Womens	135.0	2.0	1.3	25

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 200 hours from month to month. In addition, the company charges monthly inventory at the rate of 5% of the production cost based on the ending inventory levels at the end of the month. The company would like to have at least 30 units of each inventory at the end of the 2 months.

The company wants to establish a production schedule that minimizes production and inventory costs and satisfies the labor relations policy, demand and inventory requirements.

Using only the following decision variables (do not define any additional variables), formulate a linear programming model for this problem.

Decision Variables

X₁₁: the number of men's model produced in month 1

X₂₁: the number of women's model produced in month 1

X₁₂: the number of men's model produced in month 2

X₂₂: the number of women's model produced in month 2

W₁₁: the ending inventory of men's model at the end of month 1

W₂₁: the ending inventory of women's model at the end of month 1

W₁₂: the ending inventory of men's model at the end of month 2

W₂₂: the ending inventory of women's model at the end of month 2

Write down the objective function that minimizes the total production and inventory holding cost. Inventory holding cost in a month is computed based on the ending inventory.

Write down the constraint(s) to ensure that demand requirements are met (Hint: In each month look at what is available and what is the need).

Write down the constraint(s) to satisfy the ending inventory requirement.

Write down the constraint(s) to satisfy the labor relations requirement.

Nonnegativity.

X₁₁, X_{21 ,} X_12, X₂₂, W_11,, W₂₁, W₁₂ ,W₂₂ > 0