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:
| Jul | Aug | Sep | Oct | Nov | Dec | |
| 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.