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At a selling price of $50,$ a lamp company breaks even on total sales of $3000 .$ If the company's overhead is $1200,$ find the marginal production cost per lamp and find the profit on sales of 130 lamps.

$\$ 30$ and $\$ 3800$

Algebra

Chapter 1

Functions and their Applications

Section 3

Applications of Linear Functions

Functions

Missouri State University

Campbell 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).

03:18

02:03

The marginal cost of produ…

01:07

Compute and relate profit …

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02:55

The profit in dollars gene…

02:30

If the cost of manufacturi…

02:10

The total profit (in dolla…

03:37

Find the marginal profit f…

03:20

06:45

The Amalgamated Flashlight…

07:07

The marginal cost function…

okay. Working with applications of when you're functions, we're gonna be finding the marginal production cost per item as well as total profit, given a certain number of sales. So we're given, uh, information at the top. This particular firm has a selling price of $50 per item. They have a break even sales of 3000 and fixed overhead costs of 1200. We first want to find what are marginal cost of production is. And in order to do this, we first want to figure out what they sold in order to get their break even sales of 3000. So in order to find that we're going to take our break, even sales, which was 3000, that's their total sales that they broke even at and divide that by their cost of each item 50. And that will give us the number of items they sold to get there, which gives us 60. So that was their break even number of items. And let's call this X as we move forward next, what we want to do is figure out what are variable cost waas. So we're going to take total sales which are equal to 3000, minus our overhead costs which are 1200 to get 1800. And that is our variable costs. Variable costs. Those were overhead costs and these were total sales. From here we can take our variable costs of 1800 again divide that by the total number of items sold which we found were 60. That will give us 30. And that is our marginal cost of production. That answer is our first question. Next, we want to know if the company sells 130 items. What is their profit? To do this, we first want to find our revenue. Revenue we know is equal Teoh price times the quantity of items sold from here We have a price of 50 and we found and we're selling 130 items. So let's multiply that by ah 130 to get a revenue of 6500. Now we want our total cost. Total cost is equal Thio overhead plus our marginal cost per item times the quantity of items plugging in the values that we have. We know that d is 1200 plus our marginal cost of 30 times our total items sold, which is 1 30 in this scenario, and that gives us a total cost of 5100 to find the profit. Profit is simply revenue minus total costs, so we'll just plug in the values we just found 6500 minus 5100. And that gives us a profit equal to 1400 on the sale of 130 items.

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