A toy maker builds cars and trains. A car needs 2 hours on the moulding machine and 1 hour on the…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A toy maker builds cars and trains. A car needs hours on the moulding machine and hour on the painting bench. A train needs hour on the moulding machine and hours on the painting bench. In a day the moulding machine runs for at most hours and the painting bench for at most hours. A car earns a profit of dollars and a train earns dollars. How many of each should be made in a day for the greatest profit, and what is that profit?
Need a reminder? The key ideaShow
Name the unknowns and with their units. Write the objective, such as the profit . Write one inequality for each limit, and add and . Find the corners of the feasible region, work out at each, and choose the best. Say the plan and the value in the words of the story.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The model. Maximise dollars subject to , , and .
Step 2. The corners. From we get . Then gives , so and . The other corners are , and .
Step 3. The profit. At , . At , . At , . At , .
Step 4. Say it. Make cars and trains a day. The profit is dollars.
Check. Moulding uses hours and painting uses hours.
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