Linear Programming Questions and Answers

Partial-Year Depreciation Equipment acquired at a cost of $47,000 has an estimated residual value of $3,000 and an estimated useful life of 10 years. It was placed in service on October 1 of the current fiscal year, which ends on December 31. If necessary, round your answers to the nearest cent. a. Determine the depreciation for the current fiscal year and for the following fiscal year by the straight-line method. Depreciation Year 1 Year 2 b. Determine the depreciation for the current fiscal year and for the following fiscal year by the double-declining-balance method. Depreciation Year 1 Year 2

A large manufacturing firm is being charged with discrimination in its hiring practices. (a) What hypothesis is being tested if a jury commits a type I error by finding the firm guilty? (a) What hypothesis is being tested if a jury commits a type Il error by finding the firm guilty? (a) Choose the correct answer below. A. The evidence is inconclusive. B. The firm is guilty. C. The firm is not guilty. D. The firm is innocent.

The volume V of a cylinder is given by this formula: V=πr^2 L V is the Volume r is the cylinder's radius L is for Height Using this formula, write a C++ function named cylvol() that takes in the cylinder's radius and length as arguments and returns its volume. Include the function in a working program. Test the function in main. Function Prototype: double cylvol(double radius, double length);

One way to estimate the height of a child is to use the following formula, which uses the height of the parents: Hmale_child = ((Hmother* 13/12) + Hfather)/2 Hfemale_child = ((Hfather * 12/13) + Hmother)/2 All heights are in inches. Write a function that takes as input parameters the gender of the child, height of the mother in inches, and height of the father in inches, and outputs the estimated height of the child in inches. The user should be able to input the heights in feet and inches, and the program should output the estimated height of the child in feet and inches. Use the integer data type to store the heights.

State the Local Max and Local Min. Justify your answer with reference to the graph of this function and the sign of IRC. Provide a sketch of your function. y = (0.4 cos (1.5x -5.8) 1) + 420*-3

Q.39 Consider the Linear Programming Problem (LPP): Maximize αx₁ + x2 Subject to 2x1 + x₂ ≤ 6, - X1 + x₂ ≤ 1, x1 + x₂ < 4, x1 ≥ 0, x2 > 0, where a is a constant. If (3, 0) is the only optimal solution, then (A) α < -2 (B) -2 < α < 1 (C) 1 < α < 2 (D) α > 2

Determine the value c so that each of the following functions can serve as a probability distribution of the discrete random variable X. (a) f(x) = c(x²+5), for x = 0, 1, 2, 3

Everlyne has a personal LOC with her bank with a maximum credit limit of $8,000.00. The interest rate is prime plus 1%, and the current prime rate is 3%. Regardless of any account transaction activity, her bank requires on the first of every month for her to pay "the greater of 5% of the current balance or $100" from her checking account. She is allowed to exceed her maximum credit limit, but if she does the entire balance is subject to 22% interest until such time as the balance is restored below the credit limit. On October 1, the opening balance on her LOC was $2,600.00. She took advances of $3,600.00, $3,300.00, and $3,100.00 on October 17, November 17, and December 1, respectively. She made payments of $3,100.00, $3,300.00, and $3,600.00 on November 1, November 24, and December 16, respectively. The prime rate decreased by 0.75% on November 7. Complete the repayment schedule below by filling in the interest charges for October, November, and December.

Solve the linear programming problem. Minimize and maximize z = 10x + 40y Subject to 2x+y ≥ 56 x+y ≥ 40 x+2y ≥ 48 x, y ≥0

In a math class of six women and five men, if one person is selected at random to come to the board to show the solution to a problem, what is the probability that the student is a man?

The abacus shown on the right has "five" playing the role of "ten." Thus, 42 would be represented on the abacus as shown here. Moreover, it would be recorded as 132 and read as "one three two" and not as "one hundred thirty-two." What number would be represented if the beads on the abacus described are as shown in the diagrams on the right?

Calculate the first and second differences and determine whether the relation is linear, quadratic, or neither x y 1 -2 2 -4 3 -8 4 -16 5 -32

The parabola y = x² is reflected in the x-axis and then translated down 3 units . Write the equation of the new parabola in the form y = a(x - h)² + k. Type your answer without spaces between numbers and symbols. Use x^2 sign instead of x²

D is a narrow dish bounded by y = x² and y = x^4, with a mass density p(x,y) = xy. If (x,y) is the center of mass of the dish, find x and y.

A boat leaves port and follows a course of N80°E at 15 knots for 3 hr. Then, the boat changes to a new course of $29ºE at 18 knots for 4 hr and 40 min. Part 1 of 3 (a) How far is the boat from port? Round the answer to one decimal place if necessary. The boat is approximately nmi from port. Part 2 of 3 (b) Suppose that the boat becomes disabled. How long will it take a rescue boat to arrive if the boat leaves from port and travels 21 knots? Round to the nearest minute. The rescue boat will arrive in approximately hr min. Part 3 of 3 (c) What course should the rescue boat follow? Round the answer to one decimal place if necessary. The rescue boat should follow the heading

As a result of the pandemic, the demand for products purchased from Amazon rose. At the same time, workers' costs rose as they subjected themselves to a potential health hazard by working outside their homes. Ultimately wages at Amazon rose to at least $15 per hour. a. Draw the graphs necessary to model these impacts on the labor demand and labor supply. b. How can we ascertain whether demand or supply had the stronger impact on the rising wage Amazon paid? Explain.

For the polynomial function f(x) = (x^4) - 12(x^3) + 46x² - 60x + 25, find all local and global extrema. The only extrema point is (0,25). No local extrema exist. The local and global extrema are: (1, 0), (3, 16) and (5,0). No global extrema exist.

A company has current, trailing earnings of 2.1 per share. The company plans to reinvest 0.52, a share of the earnings, at an ROE of 0.093. If the required rate of return is 0.07, what is the present value of the firm's growth opportunities? 16.53 15.42 18.28 17.38 19.28

A firm has a required rate of return of 0.145. Its expected ROE is 0.151 and expected earnings per share are 7.4. If the firm's payout ratio is 0.5, what is the firm's sustainable or intrinsically justifiable P/E ratio? 7.971 7.194 8.489 7.557 8.198

Fool Proof Software is considering a new project whose data are shown below. The equipment that would be used has a 3-year tax life, and the allowed depreciation rates for such property are 33%, 45%, 15%, and 7% for Years 1 through 4. Revenues and other operating costs are expected to be constant over the project's 10-year expected life. What is the Year 1 cash flow? Equipment cost (depreciable basis) $48,000 Sales revenues, each year $60,000 Operating costs (excl. depr.) $25,000 Tax rate 35.0% a. $29,709 b. $28,294 c. $33,387 d. $29,426 e. $28,860

When the government makes sure that gas pumps accurately measure the amount of gas they provide, it is addressing which type of market failure? Market power Imperfect information Public goods Inequity Externalities

A bond has a duration of 5.2 and has a YTM of 0.1 when interest rates change by 120 basis points. What is the expected change in price for the bond using only this information? -0.0437 -0.0567 -0.0405 -0.0494 -0.0525

You consider buying shares in a stock which you expect to hold one year, receiving a dividend just prior to selling the shares. You have access to an analyst forecast for the stock with a target price one year from now (P1) after the dividend should be paid. 50.5 1.2 56 1.4 0.0875 0.0675 Given the analyst's forecast, is the stock over-priced, under-priced, or fairly-priced relative to its risk-adjusted expected return? Cannot determine with the information given Fairly-priced Over-priced Under-priced

You hold an annual coupon bond for 1 year, receiving the 0.065 coupon before selling. When bought it had 7 years to maturity, and the YTM was 0.075. Over the year, interest rates ROSE by 0.003 What is the total holding period return for this investment? 0.0591 0.0625 0.0607 0.0647 0.0571

You hold a 15 year bond that is callable in 7 years. The call premium is one semi-annual coupon payment, and the coupon rate is0.12. The current YTM is 0.1. What is the yield to call? 0.0928 0.0956 0.1011 0.0903 0.0986

A bond is priced at 885 and has a YTM of 0.055 when interest rates suddenly change by -20 basis points. The bond's price changes to 946 Calculate the duration for this bond. 36.3588 38.0131 32.5411 40.1037 34.4136

- Consider the following system of constraints, associated with a linear programming problem: x+2y < 12 x+y≤10 x≥0 y≥0 maximize z= x+4y

A factory manufactures two products, A and B. Each product requires the use of three machines, Machine I, Machine II, and Machine III. The time requirements and total hours available on each machine are listed below. Machine I Machine II Machine III Product A 1 2 4 Product B 2 2 2 Total Hours 76 94 176 If product A generates a profit of $40 per unit and product B a profit of $60 per unit, how many units of each product should be manufactured to maximize profit, and what is the maximum profit? To maximize profit, the factory should produce units of product A and units of product B. The maximum profit would be

Dr. Lum teaches part-time at two different community colleges, Hilltop College and Serra College. Dr. Lum can teach up to 7 classes per semester. For every class taught by him at Hilltop College, he needs to spend 3 hours per week preparing lessons and grading papers, and for each class at Serra College, he must do 4 hours of work per week. He has determined that he cannot spend more than 24 hours per week preparing lessons and grading papers. If he earns $5,000 per class at Hilltop College and $4,600 per class at Serra College, how many classes should he teach at each college to maximize his income, and what will be his income? a. Letting x be the first of the variables listed in the problem statement, and y the second, write the objective function. z= b. Graph the feasible region on paper, then list the corner points of the feasible region. (Enter ordered pairs (x, y), separated by commas.) c. Test the corner points to find the optimum value of the objective function: • The "winning" corner point is • The optimum value of the objective function is

A farmer grows wheat, barley, and oats on her farm. And can only use at most 500 acres. Each acre of wheat requires 3 days of labor and costs $21, each acre of barley requires 2 days of labor and costs $27, and each acre of oats requires 3 days of labor and costs $24. The farmer can provide no more than 1200 days of labor and can afford to spend no more than $15,120. In addition, because of the commodities market and demand, she will only be able to sell at most 120 acres of barley. She will be able to sell an unlimited amount of wheat and oats. If the expected profit is $50 for each acre of wheat, $40 for each acre of barley, and $45 for each acre of oats, what is the maximum profit?

John wishes to choose a combination of two types of cereals for breakfast - Cereal A and Cereal B. A small box (one serving) of Cereal A costs $0.55 and contains 10 units of vitamins, 5 units of minerals, and 15 calories. A small box (one serving) of Cereal B costs $0.40 and contains 5 units of vitamins, 10 units of minerals, and 15 calories. John wants to buy enough boxes to have at least 450 vitamins, 575 minerals, and 1050 calories. How many boxes of each food should he buy to minimize cost, and what is the minimum cost? To minimize his cost, John should buy boxes of Cereal A and boxes of Cereal B. The minimum cost would be

A factory manufactures chairs and tables, each requiring the use of three operations: Cutting, Assembly, and Finishing. The first operation can be used at most 42 hours; the second at most 42 hours; and the third at most 26 hours. A chair requires 1 hour of cutting, 2 hours of assembly, and 1 hour of finishing; a table needs 2 hours of cutting, 1 hour of assembly, and 1 hour of finishing. If the profit is $24 per unit for a chair and $34 for a table, how many units of each should be manufactured to maximize profit? To maximize profit, the factory should manufacture chairs and tables. The maximum profit would then be

Identify all methods that can possibly be used to solve a quadratic equation. Check all that applied. Plug in 0 into x. Factoring Find the slope of the line. Completing the square Quadratic formula Square Root Property

A bond has a duration of 7.65 and has a YTM of 0.08 when interest rates change by 100 basis points. What is the expected change in price for the bond using only this information? -0.0758 O -0.0614 O-0.0708 -0.0653 -0.0805

Determine the solution region for the following system of linear inqeualities by inputting a point in that region. The graph, without shaded solution, is shown on the right. (Enter an ordered pair (x, y) with integer values, that is, no decimals or fractions.) (Do not enter a point that is actually on one of the lines; keep it in the interior of the solution region.) -4x - y ≤ 5 2x + 4y ≥ 8 Point in the Solution Region:

Graph the following system of linear inequalities on paper, then answer the questions that follow. -2x - 3y > 6 (1) -5x + 4y -31 (2) The graph of line 1 is ______ The graph of line 2 is _____ (Enter an ordered pair (x, y) with integer values, that is, no decimals or fractions.) (Do not enter a point that is actually on one of the lines; keep it in the solution region.) Point in the Solution Region:

How would you explain to a student that filling in the boxes in part (a) and (b) are related? (a) -3=26 (b)=29-3 Choose the choice below that best explains the relation between the two equations above. COLLE A. Both equations can be solved using subtraction. OB. The square box is always the answer, 3 is always the subtrahend, and the remaining value is always the minuend. OC. When given two of the three, subtrahend, minuend, and answer, the third value can be found. OD. Subtraction is commutative. Therefore, both sides of the equation can be reversed.

Let f (x) = -² -1 -2x and g(x) = x + 5 Find (f g) (x) and the restriction for the domain. O (f-g) (r) = -² -3r-6 Domain restriction: -5 O (f-g) (x) = -x² - 3x + 4 No restriction for the domain. O (f-g) (x) = -2² - 3r-6 No restriction for the domain. O (f-g)(x) = -x²-3x - 6 Domain restriction: -1, -5

Minimize C=-9x + 2y subject to 3x + y ≤ 16, 2x - y ≤ -1, x, y>=0.

Sketch the solution to 27 + 86, using (a) mats, strips, and units. Draw a square for a mat, a vertical line segment for a strip, and a dot for a unit. (b) place-value cards marked 1s, 10s, and 100s from right to left. (a) Sketch the solution to 27 +86, usingmats, strips, and units. Draw a square for a mat, a vertical line segment for a strip, and a dot for a unit. Choose the correct answer below. Click the icon to view the mats, strips, and units sketch B. Click the icon to view the mats, strips, and units sketch C. Click the icon to view the mats, strips, and units sketch D. Click the icon to view the mats, strips, and units sketch A.

Linear Modelling Problem: You are flvina fromRegina to Vancouver via a jet passengeraircraft.The jet you are on climbs at a steady rate of1800 feet per minute. You want to reach analtitude of 32000 feet. The regina airport'saltitude is approximately 895 feet above sealevel. 1. Write a linear model that the Altitude interms of the time in minutes after takeoff 2. How long will it take for the jet to reach32000 feet?