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MarcKrishkeMath1600practicetest1

# MarcKrishkeMath1600practicetest1 - Math1600 Test 1 Chapters...

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Math1600 Test 1 Chapters 9 and 10 Practice Test 1 1.) Suppose that the daily sales S (in dollars) t days after the end of an advertising campaign is 2400 ( ) 400 1 S t t = + + a.) Find S (0) and interpret its meaning. 2400 (0) 400 400 2400 2800 0 1 S = + = + = + Ans: S(0) = 2800. The day the advertising campaign ended the daily sales were 2800 dollars. b.) Find 7 lim ( ) t S t and interpret its meaning. 7 7 7 7 2400 2400 lim ( ) lim 400 lim400 lim 1 1 2400 400 400 300 700 7 1 t t t t S t t t = + = + + + = + = + = + Ans: 7 lim ( ) t S t =700. Seven days after the campaign the daily sales were 700 dollars. c.) Find 14 lim ( ) t S t and interpret its meaning. 14 14 14 14 2400 2400 lim ( ) lim 400 lim400 lim 1 1 2400 400 400 160 560 14 1 t t t t S t t t = + = + + + = + = + = + Ans: 14 lim ( ) t S t =560. Fourteen days after the campaign the daily sales were 560 dollars. 2.) An industry with a monopoly on a product has its average weekly costs given by 2 10,000 ( ) 60 0.03 0.00001 C x x x x = + - + The daily demand for its product is given by 120 0.015 . p x = - If production is Limited to 3000 units, complete the following table and answer the following:

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Math1600 Test 1 Chapters 9 and 10 Practice Test 1 Ans: The table has been completed for you. a.) Find the quantity that will yield maximum profit and find maximum profit. Write a sentence answer. 2 ( ) ( ) (120 0.015 ) 0.015 120 R x xp x x x x x = = - = - + 2 3 2 10,000 ( ) ( ) 60 0.03 0.00001 0.00001 0.03 60 10000 C x xC x x x x x x x x = = + - + = - + + 2 3 2 3 2 ( ) ( ) ( ) 0.015 120 0.00001 0.03 60 10000 0.00001 0.015 60 10000 P x R x C x x x x x x x x x = - = - + - + - - = - + + - 2 ( ) 0.00003 0.03 60 P x x x = - + + 2 2 ( ) 0 0.00003 0.03 60 0 0.03 0.03 4( 0.00003)60 0.03 0.0081 2( 0.00003) 0.00006 0.03 0.09 0.00006 2000 1000 P x x x x x or x = - + + = - ± - - - ± = = - - - ± = - = = - Since x cannot be negative the only solution is x = 2000 The maximum profit is 3 2 (2000) 0.00001(2000) 0.015(2000) 60(2000) 10000 90000 P = - + + - = The company will yield a maximum profit of \$90,000 from the sell of 2000 units. b.) What selling price should the company charge for the product? Write a sentence answer. (2000) 120 0.015(2000) 90 p = - = Ans: The Company should charge \$90 per unit to yield maximum profit. Units p(x) C(x) R(x) P(x) C'(x) R'(x) P'(x) 0 120 10000 0 -10000 60 120 60 500 112.5 33750 56250 22500 37.5 105 67.5 1000 105 50000 105000 55000 30 90 60 1500 97.5 66250 146250 80000 37.5 75 37.5 2000 90 90000 180000 90000 60 60 0 2500 82.5 128750 206250 77500 97.5 45 -52.5 3000 75 190000 225000 35000 150 30 -120
Math1600 Test 1 Chapters 9 and 10 Practice Test 1 c.) Your boss has noticed in the data you have presented that revenue > cost at 3000 units, and would like to continue production beyond 3000 units in order to generate more profit. Use the data to give three distinct reasons why this would be a bad idea. Write sentence answers. When x > 3000 ( ) 0 P x < , that is P(x) decreases as x increases.

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MarcKrishkeMath1600practicetest1 - Math1600 Test 1 Chapters...

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