MATH PLUS STUDY SKILLS WORKSHOP



THTR2(Submit for quiz grade) Name: Date: 07/08/2019 1. An electronics firm manufactures two types of personal computers—a standard model and a portable model. The production of a standard computer requires a capital expenditure of $400 and 40 hours of labor. The production of a portable computer requires a capital expenditure of $250 and 30 hours of labor. The firm has $20,000 capital and 2,160 labor-hours available for production of standard and portable computers.If each standard computer contributes a profit of $320 and each portable model contributes a profit of $220, What is the number of computers that will return the maximum profit? What is the maximum profit? Define the variables:What are the constraint inequalities? Inequality concerning capital expenditure: Inequality concerning labor hour:What is the objective function?Graph the feasibility region.Corner (x, y)Amount of Profit e) No of standard computers: _____________ No of portable computers: _________________2. Use table method to solve the same problem.No of problem constraints m = Numbers of rows on the table = (m+2)(m+1)/2 = Numbers of columns on the table = (m+2) = Number of variables in the original problem= (to put that number of 0’s on the rows of table)Draw and complete your table to find the solution.3. The weekly fixed cost of manufacturing table is $1,100 and the variable cost is $54 per table. Find the total weekly cost of producing x tables. How many tables can be produced for a total weekly cost of $5150?4) Using a phone card to make a long distance call costs a flat fee of $0.85 plus $0.05 per minute starting with the first minute. Find the total cost of a phone call which lasts 10 minutes. 5) The function H described by h(x) = 2.75x + 71.48 can be used to estimate the height, in centimeters, of a woman whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the height of a woman whose humerus is 25 cm long. 6) The point at which a company's cost equals its revenue is the break-even. C represents cost, in dollars, of x units of a product. R represents the revenue, in dollars, for the sale of x units. C(x) = 12x + 120 R(x) = 24x - 600a. Graph in window 0 ≤ x ≤ 100; 0 ≤ y ≤ 1000 b. Find the number of units that must be produced and sold in order to break even.c. indicate profit and loss area and break-even point on the graph.7) The total revenue R(x) = 60x - 0.4 and the total cost C(x) = 20x - 12. Find the profit function and find P(90). 8) Find the equation of all the vertical and horizontal asymptote for f(x) = 9) Find the equation of the line with slope of - 3/5 and passing through (4, 0).10) Solve the given equation for y then find the slope, x and y intercepts of the line 3x + 4y = 12.11) a) Convert the equation y = x2 - 8x +10 to vertex form y = a(x - h)2 + k. [h = -b/2a; k = f(h)] b) Describe a way to graph the converted equation without any graphing tool starting with y = x2. c) Draw the graph.d) Does it have a maximum or minimum value?e) Find the maximum or minimum value?f) Find the x and y-intercepts.12) Find the equation for the graph in the form y = a + k, here a is either 1 or -1 and h and k are integers.A) y = - 4B) y = - 4C) y = + 6D) y = - 613) The shape of y = is shifted 5 units to the left. Then the graph is shifted 7 units upward. Find the equation for the a graph with the given transformations.A) f(x) = + 7 B) f(x) = 7 C) f(x) = + 7 D) f(x) = + 514) A company manufactures memory chips for microcomputers. Its marketing research department, produced the following price–demand function: P(x) = 75 - 3x 0 ≤ x ≤ 25Find the company’s revenue function R(x) and indicate its domain.The cost function for producing and selling x million memory chips: C(x) = 125 + 15x (in million dollars). The fixed cost is : ______$ variable cost per item:__________.(C) Write a profit function for producing and selling x million memory chips and indicate its domain.(D) Graph the Cost, Revenue, and Profit function on the same plane. Indicate the region of Loss, Profit, identify the break – even.15. Given the rational function: fx= 3x2+8x-9x2-6x+5;(A) Find the domain. (B) Find the x and y intercepts.(C) Find the equations of all vertical asymptotes.(D) If there is a horizontal asymptote, find its equation.(E) Using the information from (A)–(D) and additional points as necessary, sketch a graph of f for -10 ≤ x ≤ 10.16. Financial analysts in a company that manufactures DVD players arrived at the following daily cost equation for manufacturing x DVD players per day: C(x) = x2 + 2x + 2,000The average cost per unit at a production level of x players per day is C (x) = C(x)x(A) Find the rational function C (x).(B) Graph C (x) on your calculator.(C) Graph the average cost function C (x) on a graphing calculator and use an appropriate command to find the dailyproduction level (to the nearest integer) at which the average cost per player is at a minimum. What is the minimum average cost to the nearest cent?Answer1.(30,32)2. (30,32)3. c(x) = 1100+54x, $754. $1.355.1789.75cm6. 60 unit7. P(x) = - 0.4 + 40x + 12 , $3728. X= -1, x = -4, y = 09. Y= - 3/5 x + 12/510. Y = (12-3x)/4, Slope – ?, Xint ( 4 ,0), Yint ( 0, 3) 11. a. Y = (x - 4)2 – 6 b. Start with y = x2, shift 4 unit right, 6 unit down. D.a = 1>0, opening upward, have minimum pointe. minimum value -6, f. xint (1.55,0), (6.45,0), yint (0,10)12. b13.a14. a. R(X) = x(75-3x) ; domain 0 ≤ x ≤ 25, b. fixed cost 125, variable cost 15, c. P(X) = x(75-3x) – 125 -15x15. A. domain (-∞, 1) U (1, 5) U (5, ∞) b. xint (0.8525 ,0) yint(0, -9/5), c. x = 1, x = 5, d. y = 316. study your notes, no answers supplied intentionally ................
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