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A manufacturer of small glass figurines discovers that it costs $1,800$ for a production run of 1000 and $2200$ for a production run of 1500 . Assuming that cost is a linear function of number of items, find the overhead and the marginal cost of a figurine. Plot the cost graph.

$$C(x)=0.8 x+1000, \text { overhead }=\$ 1000, \text { Marginal } \operatorname{cost}=\$ 0.80$$

Algebra

Chapter 1

Functions and their Applications

Section 3

Applications of Linear Functions

Functions

Missouri State University

Campbell University

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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03:42

A manufacturer of vases di…

00:39

The cost function is $C(q)…

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For each cost function, fi…

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02:21

It costs 4800 to produce …

07:47

A small bottling company f…

02:58

For the cost function $C=1…

continuing with the applications of linear functions, we're gonna be deriving in the marginal cost and overhead costs from given production quantities and values. So we know that a firm is capable of producing 1000 items for $1800.1500 items for $2200 to first find our marginal cost. We want to calculate the slope, in which case the slope is equal to our marginal cost. So we can start by using the slope formula of y tu minus y one Oliver x two minus x one Plugging in our Y values will start with 2200 minus 1800 which gets divided by R X values of 1500 minus 1000 giving us 500 over, giving us 400 my bed giving us 400 over 500 equaling 20.8 a 0.8. That's going to be both our solo and our marginal cost next week and work with our cost function and by simply plugging in some of the values that we have. So we're gonna start with C of X. We have two of those actually have 1822 100 either of which will work here. Let's go ahead and use 1800 setting that equal Thio indie, which is also going to be known as our overhead costs. However, that's what you're still looking for, so we'll just leave that as D for now, adding M, which we just found with 0.8 multiplied by X, which we have, we just wanna make sure you use the coordinating one that went with our 1800 our cost using 1000 right here. We can just work this out 0.8 times. 1000 is equal to 800. Next, we can subtract 800 from both sides in order to solve for D. And as I said, that will give us our overhead costs de being cool to 1000. We've now found both our marginal costs and our overhead costs. And if we wanted to plot this, we could just mark are used. The table that's drawn above, let's say, at a value an X value of 1000. We have a Y value of 1800 and an X value of 1500. We have a Y value of 2200, and with our overhead costs. That's also the intercept of our cost function equation. So we have 1000 down here, and the line that we draw would go straight through this, which would map out, calculate out to having a slope of 0.8, and that is how you grab it.

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