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**3.3 Cost, Profit and Revenue Functions**

Learning Objective: to see how linear and quadratic functions are useful in the business world. Warm-up (IN) Write what you know about these terms – cost, demand, revenue, and profit.

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Notes! Cost (C) Revenue (R) If C=R break even R>C make a profit R<C loss of money 2 types of costs Fixed - rent, insurance, etc. Materials, wages, etc. Variable - Dependent on # of items made or hours worked

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**C= fixed costs + variable costs Cost Function -**

linear Price-Demand Function - m and n are constants (depending on the problem) linear x is the # of items that can be sold at $p per item Revenue Function - # of items sold*price per item or quadratic Profit Function - or quadratic

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**Ex 1 - Price-Demand data from a manufacturer of cameras:**

P - Wholesale price per camera x - millions of cameras sold * note as price goes down, # sold goes up a) Plot the data in the table and find the price-demand function. What is the domain?

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**b) What is the company's Revenue function for this camera**

b) What is the company's Revenue function for this camera? What is the domain of the function? c) Complete the table, computing revenues to the nearest million dollars in millions of $s in millions 1 89.79 3 239.61 6 389.94 9 450.99 12 422.76 15 305.25

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**d) Graph the revenue function and change the window appropriately**

d) Graph the revenue function and change the window appropriately. Sketch the function below. What kind of graph is it? e) What is the max revenue to the nearest $1,000? For what output of cameras (nearest thousand)? x=9.55 y=452.5 9,550,000 cameras $452,500,000 revenue

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**f) What is the wholesale price per camera to nearest dollar to produce the max revenue?**

Use the # of cameras that maximizes revenue for x! per camera g) Given the cost data below, find the cost function for manufacturing the cameras.

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**h) Find the company's profit function**

h) Find the company's profit function. Graph and find the max profit and output. Max output Max profit 7.5 million cameras $ million

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**i) Find the wholesale price for cameras to produce max profit.**

Use the # of cameras that maximizes profit for x! per camera j) Find where the company would break even, run at loss, or have a profit. break even and loss and Profit

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Out – Summary – Don’t forget about POW!! HW –

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