The Silver Star The Silver Star Bicycle Company will manufacture both men's and women's models for its Easy$-$Pedal 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:

Labor Requirements $($hours$)$

Production

Model

Costs

Manufacturing

Assembly Current

Inventory

Men's $$1202\mathrm{.}01\mathrm{.}520$

Women's $$901\mathrm{.}61\mathrm{.}030$

Last month, the company used a total of $1,000$ 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 $29$ units of each model in inventory at the end of the two months. $($Hint: Define variables for production and inventory held in each period for each product. Then use a constraint to define the relationship between these: inventory from end of previous period $+$ produced this period $-$ demand this period $=$ inventory at end of this period.$)$

$($a$)$ Establish a production schedule that minimizes production and inventory costs and satisfies the labor$-$smoothing, demand, and inventory requirements. What inventories will be maintained and what are the monthly labor requirements?

If required, round your answers to nearest whole number. If your answer is zero, enter $0.$

Production schedule: The optimal solution is as followsBicycle Company will manufacture both men's and women's models for its Easy$-$Pedal 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:

Labor Requirements $($hours$)$

Production

Model

Costs

Manufacturing

Assembly Current

Inventory

Men's $$1202\mathrm{.}01\mathrm{.}520$

Women's $$901\mathrm{.}61\mathrm{.}030$

Last month, the company used a total of $1,000$ 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 $29$ units of each model in inventory at the end of the two months. $($Hint: Define variables for production and inventory held in each period for each product. Then use a constraint to define the relationship between these: inventory from end of previous period $+$ produced this period $-$ demand this period $=$ inventory at end of this period.$)$

$($a$)$ Establish a production schedule that minimizes production and inventory costs and satisfies the labor$-$smoothing, demand, and inventory requirements. What inventories will be maintained and what are the monthly labor requirements?

If required, round your answers to nearest whole number. If your answer is zero, enter $0.$

Production schedule: The optimal solution is as follows