Activity

Question 1
A factory has to transport raw materials to a project site. The total weight of the raw material will not be less than 1,500 tons. The factory manager plans to use two different trucking firms. Big Red has heavy-duty trucks that can transport 200 tons at a cost of $50 per truckload. Common Joe is a more economical firm, costing only $20 per load, but its trucks can transport only 90 tons. The factory manager does not wish to spend more than $450 on transportation. The availability of trucks is the same for both firms.

Part A
What inequality will show the number of trucks used to transport the required raw material? Replace the inequality sign with the equal sign. Use the Edmentum Graphing Tool to graph the resulting equation and paste it into the box below. Describe which part of the graph should be shaded and whether the line should be dashed or not.

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Part B
What equation will show the manager's transportation spending limits? Replace the inequality sign with the equal sign. Use the Edmentum Graphing Tool to graph the resulting equation and paste it into the box below. Describe which part of the graph should be shaded and whether the line should be dashed or not.

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Part C
If the manager wants to use more Big Red trucks than Common Joe’s trucks, plot a graph that shows the number of trucks used, given all 3 constraints. Replace the inequality sign with the equal sign. Use the Edmentum Graphing Tool to graph all three equations and paste the resulting graph into the box below. Describe which part of the graph should be shaded and whether the lines should be dashed or not.

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Question 2
A farmer owns 30 acres of land on which he wishes to grow corn and barley. The cost per acre for seed corn is $30, and the cost per acre for barley seed is $20. The farmer can invest a maximum of $600 in seed for the two crops.

During the cultivation process, the farmer needs to spray fertilizers and insecticides specific to each crop. This costs $10 per acre for corn and $15 per acre for barley. He can invest only $400 in this process.

Part A
Write the two inequalities that are deciding factors for the number of acres of each crop the farmer will plant, based on the amount of money the farmer will spend on planting and cultivating the two crops.

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Part B
Replace the inequality signs in the two inequalities with equal signs. Plot a graph representing the two equations that influence the farmer's choice of how much of each crop to grow using the Edmentum Graphing Tool and paste it into the box below.

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