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If a manufacturer has fixed costs of $700,$ a cost per item for production of$20,$ and expects to sell at least 100 items, how should he set the selling price to guarantee breaking even?

$$\$ 27$$

Algebra

Chapter 1

Functions and their Applications

Section 3

Applications of Linear Functions

Functions

Oregon State University

Baylor University

University of Michigan - Ann Arbor

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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working with applications of linear equations. We're gonna be calculating. Ah, break even point when we have all of our information except for the price at which the seller should be selling their products in order to break even. So let's assume that we have a manufacturer who is fixed. Costs are $700. Their cost of production for item is $20 and this manufacturer wants to sell no less than 100 items. So to begin, we first can start by understanding that calculating break even points requires us to know our cost function and our revenue function. Because we said Thies equal to one another in order to calculate our break even point, begin by calculating a cost function which we can know as being equal to our overhead costs, plus our cost per item to produce times the number of items. Now, what's nice about this particular problem is we have we know all of these variables already so we can just plug them in for our overhead costs. We know that those are $700 and we know that our price per item of production is 20 and our seller wants to produce no less than 100 items. Let's assume he's producing 100 items right here. All we have to do is solve for this right here in order to get our total cost. And in doing so, we get 700 plus 2000, which case our costs are equal to 2700. That gives us one piece of information that we're gonna be needing in order to solve for our break even point. In order to get our revenue function, we know that revenue functions are equal. Thio our selling price of the item times our quantity of items. In this case, we only have one of our variables. So we have. We know that X is equal to 100 so we end up with 100 times p. Yeah, and that gives us a revenue function now if we wanted to solve for our break even point, all we have to do is set these equal to one another. We end up with 2700 being set equal to 100 p and in order to find the price at which are manufactured, should be selling his items in order to break even. Let's divide both sides by 100 to give us a price of $27. What

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