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 model the situation described, you can create a step function that accounts for the different pricing tiers based on weight. Here's how you can generate the function:
Let's denote the weight of the shipment as 'w' in pounds.
For weights less than or equal to 1 pound, the cost is fixed at $4.
For weights greater than 1 pound, the cost is $4 for the first pound, and then $3 for each additional pound.
To represent this step function in equation form, you can use the following function:
f(w) = 4 + 3 * (w - 1)
In this equation, 'f(w)' represents the function that calculates the total cost of the shipment based on its weight 'w'.
To apply the function to the given examples, let's substitute the values:
For w = 0.7 pounds:
f(0.7) = 4 + 3 * (0.7 - 1) = 4
For w = 1.0 pounds:
f(1.0) = 4 + 3 * (1.0 - 1) = 4
For w = 1.3 pounds:
f(1.3) = 4 + 3 * (1.3 - 1) = 7
For w = 1.8 pounds:
f(1.8) = 4 + 3 * (1.8 - 1) = 7
For w = 2.0 pounds:
f(2.0) = 4 + 3 * (2.0 - 1) = 7
For w = 2.1 pounds:
f(2.1) = 4 + 3 * (2.1 - 1) = 10
As you can see, the function gives the correct answer for each example. The function accounts for the different pricing tiers based on weight and accurately calculates the total cost of the shipment.
To generate a function that models the given situation, we can break it down into two parts: the flat rate charge for the first pound and the additional charge for each additional pound or part thereof.
Let's define the function as follows:
- For shipments weighing less than or equal to 1 pound, the charge will be a flat rate of $4.
- For shipments weighing more than 1 pound, the charge will be $4 for the first pound and an additional $3 for each pound or part thereof.
Using this information, we can generate a stepwise function. Here's how:
Function definition:
- Let w be the weight of the shipment in pounds.
- Let C(w) be the function that calculates the charge for a shipment of weight w.
Function implementation:
1. If w <= 1:
- Charge = $4
- Return Charge
2. If w > 1:
- Calculate the number of additional pounds or part thereof:
- Additional_pounds = w - 1
- Calculate the charge for additional pounds or part thereof:
- Additional_charge = Additional_pounds * $3
- Charge = $4 (flat rate charge) + Additional_charge
- Return Charge
To summarize, the stepwise function could be represented as:
C(w) = $4 if w <= 1
$4 + (w - 1) * $3 if w > 1
By plugging in different values of w into this function, you can verify that it gives the correct charges for each scenario mentioned in the question.