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# MATH 1630 If high school precalculus and ACT math of at least 21 contact 694 MATH 1630

pellissippi state community college

GPA 3.92

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This 0 page Class Notes was uploaded by Brown Lowe on Sunday November 1, 2015. The Class Notes belongs to MATH 1630 at pellissippi state community college taught by Staff in Fall. Since its upload, it has received 19 views. For similar materials see /class/232969/math-1630-pellissippi-state-community-college in Mathematics (M) at pellissippi state community college.

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Date Created: 11/01/15

MATH 1630 BUSINESS APPLICATIONS The Ahrens FourStep Method Many students approach story problems as a dreaded enemy from which they must escape as quickly as possible Losing a few points here and there is a small price to pay to escape the literary snare But nearly all application problems that you are likely to face in life are going to be story problems You will need to analyze the problem come up with a method of solution and decide if your result makes sense It will be easier if you have a recipe in mind and you stick to the recipe My favorite recipe is the Ahrens FourStep Method This is not the only method and may not be the best method but I like it You as a smart student will probably like it also At least as long as you are in my class The soon to be famous Ahrens FourStep Method Step 1 Choose a variable for each unknown quantity and identify your variables completely If you do this step carefully you will have earned 14 of the points already Step 2 Write an equation or perhaps a system of equations in terms of your variables which summarize the problem Now you have 12 credit Step 3 Solve the equations by an appropriate method That s right 34 credit now Step 4 Review your answer to see if it makes sense Then interpret your answer in terms of the problem Use a complete sentence and be sure to include units Example 1 Cost analysis Just in Time manufactures various types of specialty clocks The Chronowave clock radio has a fixed cost of 160 and a unit cost of 10 Each clock sells for 20 The price and demand are related by the function px 50 125 x where x is the number of clocks produced and sold a Write the total cost function and use it to find the cost of manufacturing 100 clock radios Let x the number of radios made and sold Then Cx the total cost to make x radios Cx16010x C100 160 10100 1160 The total cost of manufacturing 100 radios is 1160 b How many radios can be made for 1000 1000 160 10x 840 10x 84 x Eightyfour radios can be made for 1000 The FourStep Method page 1 J Ahrens 1222006 8 Graphically nd the number of radios that can be made for 15000 Iou Plotz not 1 516818X 2 515888 xxxxxx Intersection 1hnh 1nnn They can make 1484 radios for 15000 Write the total revenue function and use it to nd the revenue realized on the sale of 250 radios Let Rx the total revenue from the sale ofx radios Rx 20x R250 20250 5000 The revenue on the sale of250 radios is 5000 How many radios must be sold to take in 1500 1500 20x so x 75 They must sell 75 radios to take in 1500 Find the pro t Jnction and use it to nd the pro t on the manufacture and sale of150 radios Let Px the pro t on the manufacture and sale ofx radios Pgtlt R00 CX Px 20x 160 10x 20x160 10x 10x160 P15010150160 1340 The pro t on the manufacture and sale of 150 radios is 1340 How many radios must be made and sold to make a pro t of1500 1500 10X 160 1660 10x X 166 One hundred sixtysix radios must be made and sold to make a pro t of1500 How many radios must be made and sold to break even Rx Cx at the break even point 20x16010x 10x160sox16 Sixteen radios must be made to break even The FourrStep Method page 2 J Ahrens 1222000 i 39 5 Just in Time is considering raising the price of the radios to 25 Remember that price and demand are related by the function px 50 125x Find the demand at the current price of 20 20 50 125x 30 125 so x 24 They will sell 24 radios if they charge 20 each Find the demand if they raise the price to 25 each 25 50 125x 25 125x so x 20 They will sell 20 radios if they raise the price to 20 each Should they raise the price to 25 or leave it at 20 Explain At 20 their profit will be P24 1024 160 80 If they raise the price to 25 the profit function will change Px 25x 160 10x 25x 160 10x 15x 160 P251520160300160140 They should raise the price because their profit will increase from 80 to 140 Example 2 Linear Depreciation ABC Does it 4 U purchased some office equipment for 15000 For tax purposes it is assumed that the depreciation is linear and that the value of the equipment after 8 years is 2500 3 Find the linear equation which relates the value of the equipment and the number of years ABC has owned the equipment Let x the number of years ABC has owned the equipment And Vx the value of the equipment after t years We can write the given information as ordered pairs When they buy the equipment t O 0 15000 After 8 years 8 2500 Find the slope m M M 715625 x17x2 078 Y Y1 mX X1 y 715000 715625x 70 715625x 15000 So the depreciation model is Vx 15625x 15000 Use the pointslope form The FourStep Method page 3 J Ahrens 1222006 MATH 1630 BUSINESS APPLICATIONS The Ahrens FourStep Method Many students approach story problems as a dreaded enemy from which they must escape as quickly as possible Losing a few points here and there is a small price to pay to escape the literary snare But nearly all application problems that you are likely to face in life are going to be story problems You will need to analyze the problem come up with a method of solution and decide if your result makes sense It will be easier if you have a recipe in mind and you stick to the recipe My favorite recipe is the Ahrens FourStep Method This is not the only method and may not be the best method but I like it You as a smart student will probably like it also At least as long as you are in my class The soon to be famous Ahrens FourStep Method Step 1 Choose a variable for each unknown quantity and identify your variables completely If you do this step carefully you will have earned 14 of the points already Step 2 Write an equation or perhaps a system of equations in terms of your variables which summarize the problem Now you have 12 credit Step 3 Solve the equations by an appropriate method That s right 34 credit now Step 4 Review your answer to see if it makes sense Then interpret your answer in terms of the problem Use a complete sentence and be sure to include units Example 1 Cost analysis Just in Time manufactures various types of specialty clocks The Chronowave clock radio has a fixed cost of 160 and a unit cost of 10 Each clock sells for 20 The price and demand are related by the function px 50 125 x where x is the number of clocks produced and sold a Write the total cost function and use it to find the cost of manufacturing 100 clock radios Let x the number of radios made and sold Then Cx the total cost to make x radios Cx16010x C100 160 10100 1160 The total cost of manufacturing 100 radios is 1160 b How many radios can be made for 1000 1000 160 10x 840 10x 84 x Eightyfour radios can be made for 1000 The FourStep Method page 1 J Ahrens 1222006 8 Graphically nd the number of radios that can be made for 15000 Iou Plotz not 1 516818X 2 515888 xxxxxx Intersection 1hnh 1nnn They can make 1484 radios for 15000 Write the total revenue function and use it to nd the revenue realized on the sale of 250 radios Let Rx the total revenue from the sale ofx radios Rx 20x R250 20250 5000 The revenue on the sale of250 radios is 5000 How many radios must be sold to take in 1500 1500 20x so x 75 They must sell 75 radios to take in 1500 Find the pro t Jnction and use it to nd the pro t on the manufacture and sale of150 radios Let Px the pro t on the manufacture and sale ofx radios Pgtlt R00 CX Px 20x 160 10x 20x160 10x 10x160 P15010150160 1340 The pro t on the manufacture and sale of 150 radios is 1340 How many radios must be made and sold to make a pro t of1500 1500 10X 160 1660 10x X 166 One hundred sixtysix radios must be made and sold to make a pro t of1500 How many radios must be made and sold to break even Rx Cx at the break even point 20x16010x 10x160sox16 Sixteen radios must be made to break even The FourrStep Method page 2 J Ahrens 1222000 i 39 5 Just in Time is considering raising the price of the radios to 25 Remember that price and demand are related by the function px 50 125x Find the demand at the current price of 20 20 50 125x 30 125 so x 24 They will sell 24 radios if they charge 20 each Find the demand if they raise the price to 25 each 25 50 125x 25 125x so x 20 They will sell 20 radios if they raise the price to 20 each Should they raise the price to 25 or leave it at 20 Explain At 20 their profit will be P24 1024 160 80 If they raise the price to 25 the profit function will change Px 25x 160 10x 25x 160 10x 15x 160 P251520160300160140 They should raise the price because their profit will increase from 80 to 140 Example 2 Linear Depreciation ABC Does it 4 U purchased some office equipment for 15000 For tax purposes it is assumed that the depreciation is linear and that the value of the equipment after 8 years is 2500 3 Find the linear equation which relates the value of the equipment and the number of years ABC has owned the equipment Let x the number of years ABC has owned the equipment And Vx the value of the equipment after t years We can write the given information as ordered pairs When they buy the equipment t O 0 15000 After 8 years 8 2500 Find the slope m M M 715625 x17x2 078 Y Y1 mX X1 y 715000 715625x 70 715625x 15000 So the depreciation model is Vx 15625x 15000 Use the pointslope form The FourStep Method page 3 J Ahrens 1222006

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