The engineer of a concrete products plant is scheduling production of a certain size concrete pipe over the next 5 months. No pipe is on hand at the beginning of the first month. The engineer wants to meet the projected demand over the 5-month period at minimum cost. Constraints are imposed on the monthly regular rate processing time and the amount of raw materials available each month, as shown in the table below:
|Pipe Required (Number of 20 foot stands)||20||30||40||20||40||30|
|Cost of labor during regular time $/hr||$15||$15||$15||$18||$18||$18|
|Cost of labor during overtime $/hr||$17||$17||$17||$20||$20||$20|
|Labor available (persons)||30||30||40||40||20||20|
|Material available (stands)||40||50||50||10||30||20|
It takes 75 hours to produce one stand of pipe, and $20 to store one stand of pipe for one month.
- a)Assume that no materials can be carried over from month to month.
- b)Assume that materials can be carried over from month to month at no cost.