A firm has to transport 1500 packages to a site. It has a number of large vans which will transport 200 packages each and a number of small vans which will transport 100 packages each.Let 𝑥 be the number of large vans and let 𝑦 be the number of small vans used.An inequality based on the number of packages transported has been found to be 200𝑥+100𝑦≥1500.The firm needs to use at least as many small vans as large vans. A second inequality has therefore been found to be 𝑦≥𝑥.These two inequalities have been plotted on the following graph. The shaded area is the area that is not required.
Question
A firm has to transport 1500 packages to a site. It has a number of large vans which will transport 200 packages each and a number of small vans which will transport 100 packages each.Let 𝑥 be the number of large vans and let 𝑦 be the number of small vans used.An inequality based on the number of packages transported has been found to be 200𝑥+100𝑦≥1500.The firm needs to use at least as many small vans as large vans. A second inequality has therefore been found to be 𝑦≥𝑥.These two inequalities have been plotted on the following graph. The shaded area is the area that is not required.
Solution
I'm sorry, but there seems to be a misunderstanding. You've mentioned a graph, but I can't see it as this is a text-based platform. However, I can help you understand the inequalities and how they would be represented on a graph.
The first inequality, 200x + 100y ≥ 1500, represents the total capacity of the vans. The firm needs to transport at least 1500 packages, and this inequality ensures that the number of large and small vans used can carry that many. On a graph, this would be a line where every point on and above the line represents a valid combination of large and small vans.
The second inequality, y ≥ x, represents the requirement that the firm needs to use at least as many small vans as large vans. On a graph, this would be a line where every point on and above the line represents a valid combination of large and small vans.
The shaded area on the graph would represent the combinations of large and small vans that the firm should not use, as they do not satisfy one or both of the inequalities.
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