Question: A car maintenance shop must decide how many oil changes and how many tune-ups can be scheduled in a typical week. The oil change takes 20 min, and the tune-up requires 100 min. The maintenance shop makes a profit of $15 on an oil change and $65 on a tune-up. What mix of services should the shop schedule if the typical week has 8000 min available for these two types of services? How, if at all, do the maximum profit and optimal production policy change if the shop is required to schedule at least 50 oil changes and 20 tune-ups? Answer: Schedule 400 oil changes and no tune-ups; schedule 300 oil changes and 20 tune-ups. How do you set up the chart and figure everything out using the following steps? Make a mixture chart for the problem. Using the mixture chart, write the profit formula and the resource- and minimum-constraint inequalities. Draw the feasible region for those constraints and find the coordinates of the corner points. Evaluate the profit information at the corner points to determine the production policy that best answers the question.
Question: A car maintenance shop must decide how many oil changes and how many tune-ups can be scheduled in a typical week. The oil change takes 20 min, and the tune-up requires 100 min. The maintenance shop makes a profit of $15 on an oil change and $65 on a tune-up. What mix of services should the shop schedule if the typical week has 8000 min available for these two types of services? How, if at all, do the maximum profit and optimal production policy change if the shop is required to schedule at least 50 oil changes and 20 tune-ups? Answer: Schedule 400 oil changes and no tune-ups; schedule 300 oil changes and 20 tune-ups. How do you set up the chart and figure everything out using the following steps? Make a mixture chart for the problem. Using the mixture chart, write the profit formula and the resource- and minimum-constraint inequalities. Draw the feasible region for those constraints and find the coordinates of the corner points. Evaluate the profit information at the corner points to determine the production policy that best answers the question.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.4: Linear Programming
Problem 29E
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Question: A car maintenance shop must decide how many oil changes and how many tune-ups can be scheduled in a typical week. The oil change takes 20 min, and the tune-up requires 100 min. The maintenance shop makes a profit of $15 on an oil change and $65 on a tune-up. What mix of services should the shop schedule if the typical week has 8000 min available for these two types of services? How, if at all, do the maximum profit and optimal production policy change if the shop is required to schedule at least 50 oil changes and 20 tune-ups?
Answer: Schedule 400 oil changes and no tune-ups; schedule 300 oil changes and 20 tune-ups.
How do you set up the chart and figure everything out using the following steps?
- Make a mixture chart for the problem.
- Using the mixture chart, write the profit formula and the resource- and minimum-constraint inequalities.
- Draw the feasible region for those constraints and find the coordinates of the corner points.
- Evaluate the profit information at the corner points to determine the production policy that best answers the question.
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