WidgetsRUs is deciding on a widget production schedule for the next three days. They currently have 0 widgets in inventory and they are looking to satisfy a demand of 100 widgets at the end of day 3. Worker 1 is scheduled to work on days 1 and 2 and Worker 2 is scheduled to work on days 2 and 3. Each worker produces 3 widgets an hour, and is allowed to work at most 14 hours on a single day and at most 24 hours over the three day production period. Further, the total labor (hours worked by both workers) on any day cannot exceed 20 hours. On day 1 the workers are paid $10 an hour, on day 2 they are paid $8 an hour and on day 3 the workers are paid $7 an hour.
Find a labor schedule for both workers which minimizes labor costs while still meeting the 100 units of demand at the end of day 3. Formulate the problem as a linear program. Solve the problem in excel and use the sensitivity report to answer the following questions which you may assume are all independent.
You receive a request for an extra 2 widgets at price of $3 per widget (assume the additional profit from this sale would be $6). Should you increase production to 102 widgets?
How much does the hourly wage on day 1 need to decrease in order to start producing on day 1 in the optimal solution?