Finite Mathematics MAT 1304

FINITE MATHEMATICS 15

FiniteMathematics MAT 1304

Question1Find the slope of the line passing through the given pair ofpoints (6,2) and (9,1)slope = (2-1)/ (6- 9) = -1/3

d. -1/3Q2.Find the slope of the line passing through thegiven pair (7,2) and (9,2)slope = (2-2)/9 – 7) = 0/2 = 0

d.0Q3.Find the slope of the line. A line perpendicular to3x = 4y + 6slope of 3x = 4y + 6 is 3/4 since the equation canbe rewritten as y = 3/4x – 1.5

Therefore,the slope of the perpendicular line to 3x = 4y + 6 is -4/3

c.-4/3Q4.Find the slope of the line 5x + 2y = – 16

theline can be written as y = mx + c as follows 2y = -5x -16. Dividingthrough by 2, the equation will be as follows, y = -5/2x – 8.Therefore slope is -5/2a. -5/2Q5.Findan equation in slope-intercept form (where possible) for theline.Through (3, – 5), m= – 2

Sincem= -2, then the slope of the line is -2

Theequation would be (y + 5)/ (x – 3) = -2

Y+ 5 = -2 (x – 3)

Y= -2x + 6 – 5

Y= -2x + 1d. y= 2x + 1Q6.Find an equation inslope-intercept form (where possible) for the line.Through (5,2) and (- 10, 2)

Slope= (2- 2)/ (5 + 10) = 0

Equation(y – 2/(x – 5) = 0

Y– 2 = 0

Y= 2c. y = 2Q7.Findthe slope of the line (Graph)

Intervals(1, 0) and (0 -3)

Slope= (0 + 3)/ (1 – 0) = 3a.3Q8.Find the slopeof the line. (Graph)b. undefined Q9.Evaluatethe function as indicatedFind f (- 3) when f(x) = – 6x- 7

F(-3) = -6 (-3) – 7

=18– 7

=11a.11Q.10Write a cost function for the problem.Assume that the relationship is linear.A moving firm charges aflat fee of \$30 plus \$25 per hour. Let C(x) be the cost in dollars ofusing the moving firm for x hours.C(x) = 25x + 30d. C(x)= 25x + 30Q11.Let the demand and supply functionsbe represented by D(p) and S(p), where p is the price in dollars.Find the equilibrium price and equilibrium quantity for the givenfunctions.D (p) = 6,272- 50pS(p) = 230p -1,568Equilibrium price at equilibrium, D(p) = S(p)

Thus,6272 – 50p = 230p – 1568

6272+ 1568 = 230p + 50p

280p= 7840

P= 28

Equilibriumquantity = 6272 – 50*28 = 4872a.\$28 4,872 Q12.Supposethat the demand and price for a certain model of graphing calculatorare related by p = D(q) = 102 – 2.75q, where p is the price (indollars) and q is the demand ( in hundreds). Find the price if thedemand is 100 calculators.

P= 102 – 2.75 (1)

P= 99.25a.\$99.25Q13.A book publisher found that thecost to produce 1000 calculus textbooks is \$26,500, while the cost toproduce 2000 calculus textbooks is \$50, 900. Assume that the costC(x) is a linear function of x, the number of textbooks produced.What is the marginal cost of a calculus textbook?

Marginalcost = (50,900 – 26,500) / (2000 – 1000)

=24.40c.\$24.40Q14.A toilet manufacturer has decided to come outwith a new and improved toilet. The fixed cost for the production ofthis new toilet line is \$16,600 and the variable costs are \$63 pertoilet. The company expects to sell the toilets for \$154. Formulate afunction P(x) for the total profit from the production and sale of xtoilets.Revenue function = 154x

Costfunction TC = 63x + 16,600

Profitfunction = TR – TC

=154x – (63x + 16,600)

91x– 16,600B. P(x) = 91x -16,600Q15.NorthwestMolded molds plastic handles which cost \$1.00 per handle to mold. Thefixed cost to run the molding machine was 31,110 per week. If thecompany sells the handles for \$3.00 each, How many handles must bemolded weekly to break even?At break even, TC = TR

X+ 31110 = 3x

2x= 31110

X= 15,555d.1555 handlesQ16.The bankstemperature display shows that it is 35 degrees Celsius. What is thetemperature to the nearest degree Fahrenheit?

C=5/9(F-32)

35= 5/9 (F-32)

315= 5F – 160

475= 5F

F= 95a.95 degreesQ17.Use the echelon method tosolve the system of two equation in two unknowns.X + 8y =- 52-2x + 7y = – 57

1 8 -52

-2 7 -57

18 -52

023 -161

1 8 -52

01 -7

1 04

01 -7

b.(4, -7)Q18.Use the echelon method to solve thesystem of two equation in two unknowns.9x + 8y = 18-6x+ 3y = – 129 8 18

-6 3-12

3 11 6

-6 3 -12

111/3 2

0 250

111/3 2

01 0

10 2

0 1 0a.(2,0)Q19.Use the echelon methodto solve the systemX/2 + y/2 = 4x + y= 2

½ ½ 4

1 1 2

1 1 4

1 12

Thepair has no solution since the matrix cannot be expressed in echelonformd. No solutionQ20.There were 440 peopleat a play. The admission price was \$3 for adults and \$1 for children.The admission receipts were \$1,020. How many adults and how manychildren attended?

Letthe number of adults be x and that of children be y

X+ y = 440

3x+ y = 1020

2x= 580

X= 290

Y= 440 – 290

Y= 150d.290 adults, 150 childrenQ21.Find theequation of the line that passes through the point(-2, 5) thatis parallel to the line 3x + 4y = 20. Write the final answer in slopeintercept form. (Show work)parallel lines have the same slopethe gradient of 3x +4y =20 is -3/4 since the equation can be writtenas y = -3/4x +5. Therefore, the gradient of the other line is -3/4

Equationof the line (y – 5)/ (x + 2) = -3/4

4(y– 5) = -3 (x + 2)

4y– 20 = -3x – 64y = -3x + 14

Y= -3/4x + 7/2Q22.The sales of a small company were\$27,000 in its second year of operation and \$63,000 in its fifthyear. Let y represent sales in the xth year of operation. Assume thatthe data can be approximated by a straight line.Find theslope of sales line. (Show Work).Slope = (63,000 – 27,000)/(5 – 2)

36,000/312,000Q23.Assumethat the situation can be expressed as a linear cost function. Findthe cost function. (Show Work).Fixed cost: \$100 50 itemscost \$1600 to produce.variable cost = TC – FC = 1600 – 100= 1500variable of producing 1 item = 1500/50 = 3

Costfunction C(x) = 3x + \$100Q24.Show all work associatedwith this problem.Producing x units of tacos cost C(x)=5x+20 revenue is R(x) =15x, Where both C(x) and R(x) are indollars. How many tacos need to be sold in order to make a profit of\$500? (Show work).Profit function = 15x – (5x + 20)=10x– 20

Unitsto be sold for a profit of 500 10x – 20 = 500

10x= 520

=52 unitsQ25.Use the echelon method to solve eachsystem of two equation in two unknowns. (Show work checkanswer)12x – 5y = 93x – 8y = – 1812 -5 9

3-8 -18

3 19 63

3 -8 -18

1 19/3 21

3 -8-18

119/3 21

1 -8/3 -6

1 19/3 21

09 27

1 19/3 21

0 1 31 02

0 1 3ordered pair (2, 3)

X= 2 and Y = 3

References

Lial,M. L., Greenwell, R. N., &amp Ritchey, N. P. (2012). Finitemathematics (10th ed.). Boston, MA: Pearson Education.