A Lab 1.6 day2 Interpret Marg Cost Rev Profit class 3 PDF

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Marginal Cost and Revenue Online homework Assignment from Professor Poracky MA117...

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MATH 117

Interpreting Cost, Revenue and Profit

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In each of the following functions, let x = the number of items. For the cost function: Suppose

C ( x) 140  6 x

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The marginal cost is 6 . This means cost is $6 per item made. C . The slope of the cost function has the form x If I produce one more item, my cost will increase by $6.

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The C-intercept is (0, 140) . This means my fixed (or start-up) costs are $140.

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For the revenue function: Suppose

R( x) 11x

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The selling price is $11. The marginal revenue is 11. This means $11 per item sold.

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The slope of the revenue function has the form

 

R . x If I sell one more item, my revenue will increase by $11. The R-intercept is (0, 0). This means no revenue if no items are sold.

For the profit function: Suppose P( x) 5 x  140    

The marginal profit is 5. This means $5 profit per item made and sold. P . The slope of the profit function has the form x If I produce and sell one more item, my profit will increase by $5. The P-intercept is (0, -140). This means a loss of $140 if items are sold.

Interpreting cost, revenue and profit for a specific number of items:  C (30) 320 If I produce 30 items, it costs me $320. Write ordered pair (30, 320).  R(30) 330 If I sell 30 items, my revenue will be $330. (30, 330).  P(30) 10 If I produce and sell 30 items, my profit will be $10. (30, 10). Break-even analysis - The break-even point can be found by:  Letting cost equal revenue. For C ( x) 140  6 x and R( x) 11x , let C = R. Solve the equation 140  6 x 11x . Substitute back to find C and then R.  The break-even point is (28, 308). If I make and produce 28 items, then both my cost and revenue are $308.  Letting the profit function equal zero. For P( x) 5 x  140, let P = 0. Solve 5 x  140 0  If I make and produce 28 items, then profit = $0. (This method doesn’t find the $R and $C) Find the Profit function, given the Revenue and Cost functions. P = R - C Show middle steps of work. P = 11x - (140  6 x) = 5 x  140...