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A contractor has the task of loading containers onto a truck - Leaving Cert Mathematics - Question (b) - 2010
Question (b)
A contractor has the task of loading containers onto a truck. There are two types of container: heavy containers which weigh 160 kg each and light containers which w... show full transcript
Worked Solution & Example Answer:A contractor has the task of loading containers onto a truck - Leaving Cert Mathematics - Question (b) - 2010
Step 1
Step 2
The contractor charges €48 to load each heavy container and €36 to load each light container. How many of each should be loaded in order to maximise income?
Answer
The income function can be expressed as:
To maximize income, plot the inequalities on a graph and identify the feasible region. Solving the vertices will give the maximum income configuration:
- Compute intersections of the lines from the inequalities:
- Solving the two inequalities gives points like (0, 0), (13, 0), (0, 27), and (10, 12).
- Evaluate income at each vertex to determine the maximum:
- At (0, 0): 0
- At (0, 27): 972
- At (10, 12): 912
- The maximum income occurs at (0, 27) with an income of €972.
Step 3
On your graph, show the region where the income is at most €576.
Answer
To find the region where income is at most €576, rewrite the income equation:
Plot this line on the graph along with the previously established inequalities. The shaded area under this line, along with the feasible region defined by the weight and time constraints, indicates the region where the income does not exceed €576.