1. Draw the following lines gives slope= 2, y intercept = 0. Measure the point where each line cuts the horizontal axis.
(Teresa Bradley., Essential Mathematics for Economics and Business., Jhon Wiley & Sons., Third Ediition., p 43 number 3)  linear function and application no 1

2. Draw the following lines gives slope= -1, y intercept = 2. Measure the point where each line cuts the horizontal axis (page 43 number 6)
(Teresa Bradley., Essential Mathematics for Economics and Business., Jhon Wiley & Sons., Third Ediition., p 43 number 6) linear function and application no 2

3. Given the equation of the line y= x +2
(a) Write down the slope and intercepts (horizontal and vertical) for each line
(b) Calculate the values of y when x = -2,0, 2, 4, 6
(c) Plot the line over the interval x = -2 to x = 6(Teresa Bradley., Essential Mathematics for Economics and Business., Jhon Wiley & Sons., Third Ediition., p 55 number 2a) linear function and application no 3

4. Write the equation of y=2 in the form y = f(x), hence write down the slope, intercepts (if any)
(Teresa Bradley., Essential Mathematics for Economics and Business., Jhon Wiley & Sons., Third Ediition., p 55 number 3a) linear function and application no 4

5. Write the equation 5x + y + 4= 0 in the form y = f(x), hence write down the slope, intercepts (if any)
(Teresa Bradley., Essential Mathematics for Economics and Business., Jhon Wiley & Sons., Third Ediition., p 55 number 3c) linear function and application no 5

6. Given the equation 2y – 5x + 10 = 0
(a) Write of the equation in the form y = f(x)
(b) Calculate the intercepts, plot the line by joining the intercpes
(c) From the graph, show that the magnitude of slope is ratio vertical intercept/ horizontal intercept
(Teresa Bradley., Essential Mathematics for Economics and Business., Jhon Wiley & Sons., Third Ediition., p 55 number 4a) linear function and application no 6

7. Plot the points (2,10), (2,5), (2,1) and (2,-2) Deduce the equation of the line
(Teresa Bradley., Essential Mathematics for Economics and Business., Jhon Wiley & Sons., Third Ediition., p 55 number 7b) linear function and application no 7

8. Find the equation of a straight line pass through yhe poins (2,4) and (8,16) and plot the graph
(Teresa Bradley., Essential Mathematics for Economics and Business., Jhon Wiley & Sons., Third Ediition., p 81 number 2a) linear function and application no 8

9. It is known that the number of lunches demanded is 80 units when the price is $5 and 45 when the price is $ 12
(a)  Determine the equation of the deman function in the form Q = f(P). Plot the graph of the demand function
(b)  Use the equation of the demand function to calculate the change in demand when the price (i) increases by $ 3 (ii) decrease by $2
(c)  Estimate the decrease in price for each lunch when the number of lunches demanded (quantity demanded) increase by 15
(Teresa Bradley., essential Mathematics for Economics and Business., John Wiley & Sons., Third Edition., page 81 number 4)linear function and application no 9

10. A supplier supplies 50 football scarves when the price is $ 6 and 90 units when the price is $ 11 each
(a)  Determine the equation of the supply function in the form of P = h(Q)
(b)  How many additional scerves are sullied for each successive $1 increase in price
(c)  Calculate the quantity supplied when the price is $ 8.5 per scarf
(d)  Calculate the price when 120 scarves are supplied
(Teresa Bradley., essential Mathematics for Economics and Business., John Wiley & Sons., Third Edition., page 81 number 5) Linear function and application no 10

11. The variable cost of a product increase by $4 for each unit produced and the fixed cost are $ 64
(a)  Write down then equation for the total function
(b)  Graph the equation
(c)  What is slope of the line
(d)  Determine the total both algebraically and graphically when 10 units are produced
(Teresa Bradley., essential Mathematics for Economics and Business., John Wiley & Sons., Third Edition., page 81 number9) Linear function and application no 11

12. A distributor supplies 100 DVD’s when the price $ 15 and 125 when the price is $20 each.
(a)  Determine the equation of the supply function in the form of P = f(Q). Plot the graph of the supply function
(b)  How many additional units are supplied for each successive $ 1 increase in price
(c)  Calculate the price when 150 DVD’s are supplied
(d)  Calculate the quantity supplied when the price $ 30 per DVD
(Teresa Bradley., essential Mathematics for Economics and Business., John Wiley & Sons., Third Edition., page 82 number 10) Linear function and application no 12

13. P= 90 -0.05 Q is the demand function for graphic calculators in the engineering college.
(a)  Derive expressions for  in term of (i) P only, (ii) Q only
(b)  Calculate the value of  when the calculators priced at P = $20, $ 30, $ 70
(c)  Determine the number of calculators demanded when ;
(Teresa Bradley., essential Mathematics for Economics and Business., John Wiley & Sons., Third Edition., page 91number 5) Linear function and application no 13

14. Given the supply function P = 20 + 0,5 Q
(a)  Calculate the arc price elasticity of supply when the price increases from $ 40 to $60. Interpret your result
(b)  Calculate the percentace change in quantity supplie in response to a price increase of 10 % when P = $40
(i)   By using the definition of elasticity in equation (2.16)
(ii) Exactly by using ordinary arithmetic
(Teresa Bradley., essential Mathematics for Economics and Business., John Wiley & Sons., Third Edition., page 91 number 7) Linear function and application no 14

15. It is known that when the price of a good is $2, 50 units are demanded but when the price increase tp $4 the quantity demanded drops to 45 units (that is a line contains the points (2,50) and (4,45)
(a)  Calculate the change in demand that result from a one unit increase in price
(b)  Calculate the quantity demanded at prices of $ 5, $ 8 and $ 10 per unit
(c)  Graph the demand function
(d)  Write down the equation of the demand function in the form (i) P = g(Q) and (ii) Q = f(P)
(Teresa Bradley., essential Mathematics for Economics and Business., John Wiley & Sons., Third Edition., page 96 number 2) Linear function and application no 15

16. Pocket money of $ 5 may be spent on either ice cream or soft drinks. Ice cream costs $ 0.12 per unit while dsoft drink cost $ 0.20 prt unit
(a)  Write down the equation of the budget constraint. Graph the constraint
(b)  Show by calculation and graphically, how the budget constraint change if the price of ice cream drops to $ 0.9 while pocket money and price of soft drinks do not change
(c)  Show by calculation and graphically, how the budget constraint change if the price of soft drinks increase to $ 0.25  while pocket money and price of ice cream do not change
(d)  If the pocket money increase to $ 7.5, and the price of ice cream and soft drink remain the same, how does the budget constraint alter? Graph the new budget constraint
(Teresa Bradley., essential Mathematics for Economics and Business., John Wiley & Sons., Third Edition., page 96 number 7) Linear function and application no 16

17.Suppose consumers will demand 40 units of a product when the price is $12.75 per unit and 25 unit when the price is $18.75 each. Find the demand equation, assuming that is linear. Find the price per unit when 37 units are demanded.(Mathematical Analysis for Business, Economic and The Life and Social Sciences., Ernest F. Haueussler,Jr., Richard S. Paul., Richard J Wood, Pearson International Edition., Problem 3.2 no 15) Linear function and application no 17

18.The demand per weeks for a CD is 26,000 copies when the price is $12 each and 10,000 copies when the price is $18 each. Find the demand function for the CD, assuming that isi linear
(Mathematical Analysis for Business, Economic and The Life and Social Sciences., Ernest F. Haueussler,Jr., Richard S. Paul., Richard J Wood, Pearson International Edition., Problem 3.2 no 16) Linear function and application no 18

19. A Refrigator manufacturer will produce 3000 units when the price is $ 940, and 2200 units when the price is $740. Assume the price (Q) and the quantity (Q) produced are linearity related and find the supply function
(Mathematical Analysis for Business, Economic and The Life and Social Sciences., Ernest F. Haueussler,Jr., Richard S. Paul., Richard J Wood, Pearson International Edition., Problem 3.2 no 17) Linear function and application no 19

20 Suppose a manufacturer of shoes will place on the market 50 (thousand pairs) when the price is 35 (dollar per pair) and 35 when the price is 30. Find the supply equation, assuming that price (P) and the quantity (Q) are linearly related.
(Mathematical Analysis for Business, Economic and The Life and Social Sciences., Ernest F. Haueussler,Jr., Richard S. Paul., Richard J Wood, Pearson International Edition., Problem 3.2 no 18) Linear function and application no 20

 

21. Suppose the cost to produce 10 units of a product is $40 and the cost of 20 units is $70. If cost, C, is linearity related to output, C find a linear eguation relating C dan Q. Find cost to produce 35 unit
(Mathematical Analysis for Business, Economic and The Life and Social Sciences., Ernest F. Haueussler,Jr., Richard S. Paul., Richard J Wood, Pearson International Edition., Problem 3.2 no 19) Linear function and application no 21

22. An advertiser goes to a printer and is charge $79 for 100 copies of one flyer and $88 for 400 copies of another flyer, This printer charges a fixed setup cost plus a charge for every copy of sinle page flyer. Find a function that describes the cost of a printing job, if x is the number of copies made.
(Mathematical Analysis for Business, Economic and The Life and Social Sciences., Ernest F. Haueussler,Jr., Richard S. Paul., Richard J Wood, Pearson International Edition., Problem 3.2 no 20) Linear function and application no 22

 23An electric utility company charges residential customers 12.5 cents perkilowatt- hour plus a base charge each month. One customer’s monthly bill comes $ 51.65 for 380 kilowatt. Find a linear function that describes the total monthly charges for electricity if x isi the number of kilowatt-hours used in a month
(Mathematical Analysis for Business, Economic and The Life and Social Sciences., Ernest F. Haueussler,Jr., Richard S. Paul., Richard J Wood, Pearson International Edition., Problem 3.2 no 21) Linear function and application no 23

24. A cancer patient is to receive drug and radiation therapies. Each cubic centimeter of a drug to be used contain 210 curative units and each minute of radiation exposure gives 305 curative units. The patient requires 2410 curative units. If d cubic centimeters of the drug and r minutes of radiation are administered,determine an equation relation d and r. Graphy the equation for d  and r , the label of horizontal axis as d
(Mathematical Analysis for Business, Economic and The Life and Social Sciences., Ernest F. Haueussler,Jr., Richard S. Paul., Richard J Wood, Pearson International Edition., Problem 3.2 no 22) Linear function and application no 24

25. Suppose the value of a mountain bike decreases each year by 10% of its original value. If the original value is $ 1,800. Find an equation that expresses the value v of the bike t years after purchase, where . Sketch the equation, choosing t as the horizontal axis and v as the vertical axis. What is the slope of resulting line.
(Mathematical Analysis for Business, Economic and The Life and Social Sciences., Ernest F. Haueussler,Jr., Richard S. Paul., Richard J Wood, Pearson International Edition., Problem 3.2 no 22) Linear function and application no 25

26. A new television depreciates $ 120 per year, and its worth $340 after four years. Find a function that describes the value of this television, if x is the age of the television in years.
(Mathematical Analysis for Business, Economic and The Life and Social Sciences., Ernest F. Haueussler,Jr., Richard S. Paul., Richard J Wood, Pearson International Edition., Problem 3.2 no 23) Linear function and application no 26

 

27. A new apartment building was sold for $ 960,000 five years after it was purchased . The original owners calculated that the building appreciated $ 45,000 per year while they owned it. Find a linear function that describes the appreciation of the building, if x is the number of years since the original purchase

(Mathematical Analysis for Business, Economic and The Life and Social Sciences., Ernest F. Haueussler,Jr., Richard S. Paul., Richard J Wood, Pearson International Edition., Problem 3.2 no 24) Linear function and application no 27

 

28. A house purchased for $ 245,000 is expected tp double in value in 15 years. Find a linear equation that describes the house’s value after t years

(Mathematical Analysis for Business, Economic and The Life and Social Sciences., Ernest F. Haueussler,Jr., Richard S. Paul., Richard J Wood, Pearson International Edition., Problem 3.2 no 25) Linear function and application no 28