The profit P (in dollars) from selling P laptop computers is given by -0.04x2 +

Question

The profit P (in dollars) from selling P laptop computers is given by -0.04x2 + 25x-1500 1. a. Find the additional profit when the sales increase from150 to 151 units b. Find the marginal profit when x = 150 c. Compare the results of part (a) and (b) 2. Use the information in the table to find the models and answer the question belovw Marginal revenue (MR) Price (p) Total revenue (TR) Quantity produced and sold (Q) 0 160 140 120 100 80 60 0 280 480 600 640 600 130 90 50 10 4 10 Use graphing utility (or your graphing calculator) to find the quadratic model that relates the total revenue (TR) to the quantity produced and sold (Q) Using derivatives, find a model for marginal revenue from the model you found in part a. b. Calculate the marginal revenue for all values of Q using your model in part (b), and compare these values with the actual values given. How good is your model? c.

Explanation / Answer

1. The profit P from selling x laptop computers is:

. .P = -0.04 x2 + 25 x - 1500

(a) Profit for sales x = 150 is

. .P = -0.04 (150)2 + 25 (150) - 1500 = $ 1350

Profit for sales x = 151 is

. .P = -0.04 (150)2 + 25 (150) - 1500 = $ 1362.96

Therefore, additional profit when sales is increased from 150 to 151

. .= $1362.96 - $ 1350 = $ 12.96

(b) For marginal profit differentiating Profit function P, with respect to x, we have

. .P' = -0.08 x + 25

Therefore, marginal profit at x = 150 is

. .P' = -0.08 (150) + 25 = $ 13

(c)  From parts (a) and (b), we see that the marginal profit is greater than the additional profit on sales of 1 unit (x = 150 to x = 151)

and this difference amount is:

. = $ 13 - $ 12.96 = $ 0.04

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