GENERATE A FUNCTION THAT MODELS THE SITUATION. Consider the type of function described—it is not linear!
A shipping company charges $4 for the first pound and $3 for each additional pound or part thereof.
As you try to come up with the equation, consider the following:
-How much should you be charged if your shipment weighs 0.7 pounds? $4
-How much should you be charged if your shipment weighs 1.0 pounds? $4
-How much should you be charged if your shipment weighs 1.3 pounds? $7
-How much should you be charged if your shipment weighs 1.8 pounds? $7
-How much should you be charged if your shipment weighs 2.0 pounds? $7
-How much should you be charged if your shipment weighs 2.1 pounds? $10
Make sure that your function gives the correct answer for each of these.
Can someone pease help, all I could figure out was that the function uses linear programming and that its a step-wise function too. But I don't know how to generate the function for this. I asked before but MathMe only said how to graph it which I already know. Thanks for the help. :)
To generate a function that models the given situation, you can break down the problem into two parts:
1. For the first pound: The company charges a flat fee of $4 for the first pound, regardless of the weight. So, for any shipment that weighs less than 1 pound, the charge will be $4.
2. For each additional pound: The company charges $3 for each additional pound or part thereof. This means that if the weight of the shipment exceeds 1 pound, you need to calculate the additional weight beyond 1 pound and multiply it by $3. For example, if the shipment weighs 1.3 pounds, the additional weight beyond 1 pound is 0.3 pounds, so the additional charge would be $3 times 0.3.
Combining these two parts, the function that models the situation is as follows:
- If weight <= 1 pound, the charge = $4.
- If weight > 1 pound, the charge = $4 + ($3 * (weight - 1)).
In this function, "weight" represents the weight of the shipment in pounds.
Let's test this function using the given examples:
- For a shipment weighing 0.7 pounds: The weight is less than 1 pound, so the charge is $4, which matches the given information.
- For a shipment weighing 1.0 pounds: The weight is exactly 1 pound, so the charge is $4, as expected.
- For a shipment weighing 1.3 pounds: The weight is more than 1 pound, so the additional weight beyond 1 pound is 0.3 pounds. The charge would be $4 (for the first pound) plus $3 times 0.3, which equals $7, as expected.
- For a shipment weighing 1.8 pounds: The weight is more than 1 pound, so the additional weight beyond 1 pound is 0.8 pounds. The charge would be $4 (for the first pound) plus $3 times 0.8, which is $7, as expected.
- For a shipment weighing 2.0 pounds: The weight is more than 1 pound, so the additional weight beyond 1 pound is 1.0 pound. The charge would be $4 (for the first pound) plus $3 times 1.0, which equals $7, as expected.
- For a shipment weighing 2.1 pounds: The weight is more than 1 pound, so the additional weight beyond 1 pound is 1.1 pounds. The charge would be $4 (for the first pound) plus $3 times 1.1, which equals $10, as expected.
Therefore, this function accurately models the given situation.