​​​​1. f(x) = 1/2x-3 or y = 1/2x -3

1. The input is x and the output is f(x) or y. What is the slope of the function?
2. What is the y-intercept of the function?
3. What is the x-intercept of the function?
4. Graph the function.

1. What is the slope of a horizontal line?
2. Determine whether each function is increasing or decreasing?

f(x) = 4x + 3

a(x) = 5 -2x

k(x) = -4x +1

p(x) = 1/4x-3

q(x) = 4

4.

1. Find a linear equation satisfying the following condition

Passes through (2, 4) and (4, 10)

What is the solution to the following system of linear equations

2x+y = 15

3z -y = 5

Solve the system of equations by graphing

1. Find the midpoint of the line segment with the endpoints (7, -2) and (9, 5)
2. Find the midpoint of the line segment with endpoints (-2, -1) and (-8, 6).
3. If we invest $3,000 in an investment account paying 3% interest compounded quarterly, how much will the account be worth in 10 years?

1. From period 1 to period 2, weekly income increased from $100 to $106.5. What is the percentage change in income?
2. From period 1 to period 2, hourly wage increased from $12 to $15. What is the percentage change in hourly wage?

VSB 3006 – Dr. JME

Handout - Breakeven

                                        #1                #2               #3

Selling Price of A             10                 15                 6

Selling Price of B             8                  22                5

Variable Cost of A           4                  11                 4

Variable Cost of B            7                  19                 4

Mix of A and B                 5-2               3-5               2-1

Fixed Costs                      1,700            2,000           1,000

Tax Rate                          25%             30%             30%

Desired NI                      10,000          45,000         28,000

Required: Determine the number of As and Bs each of the firms should sell to meet their individual goals.

A spring with a 4-kg mass and a damping constant 3 can be held stretched 1 meters beyond its natural length by a force of 4 newtons. Suppose the spring is stretched 2 meters beyond its natural length and then released with zero velocity, In the notation of the text, what is the value ?2−4??c2−4mk?  m2kg2/sec2m2kg2/sec2 Find the position of the mass, in meters, after t seconds. Your answer should be a function of the variable t with the general form ?1???cos(??)+?2???sin(??)c1eαtcos⁡(βt)+c2eγtsin⁡(δt)

Four different types of insecticides are used on strawberry plants. The number of strawberries on each randomly selected plant is given below. Find the test statistic F to test the hypothesis that the type of insecticide makes no difference in the mean number of strawberries per plant. Use α = 0.01.

STEP 1: Hypothesis: Ho:______________________________________ H1:______________________________________

STEP 2: Restate the level of significance: _______________________

STEP 4: p-value __________________________ from appropriate test on calculator.

STEP 5: Conclusion.

Profit-maximizing Q (quantity) and P (price)

will you get a different Q and P if you use equations 2 and 4 vs. equations 2, 3, and 5?

(1) Demand: Q = 230 – 2.5P + 4*Ps + .5*I, where Ps = 2.5, I = 20.

(2) Inverse demand function [P=f(Q)], holding other factors (Ps = 2.5 and I =20) constant, is, P=100-.4*Q.

(3) Production: Q = 1.2*L - .004L2 + 4*K - .002K2;

(4) Long Run Total Cost: LRTC = 2.46*Q + .00025*Q2 (Note: there are no Fixed Costs);

(5) Total Cost: TC = 1*L + 10*K.

Use elementary row or column operations to evaluate the following determinant. You may use a calculator to do the multiplications. 1 -9 6 -9 -5 2 -17 6 -21 -11 2 -13 4 -17 -12 0 6 4 2 0 0 -2 16 8 2

Integration Exercise 2 Different Costs for Different Purposes, Cost-Volume-Profit-Relationships [LO 1-1, LO 1-2, LO 1-3, LO 1-4, LO 1-5, LO 1-6, LO 5-1, LO 5-3, LO 5-5, LO 5-7, LO 5-8]

Hixson Company manufactures and sells one product for $34 per unit. The company maintains no beginning or ending inventories and its relevant range of production is 20,000 units to 30,000 units. When Hixson produces and sells 25,000 units, its unit costs are as follows:

Required:

1. For financial accounting purposes, what is the total amount of product costs incurred to make 25,000 units? What is the total amount of period costs incurred to sell 25,000 units?

2. If 24,000 units are produced, what is the variable manufacturing cost per unit produced? What is the average fixed manufacturing cost per unit produced? (Round your answers to 2 decimal places.)

3. If 26,000 units are produced, what is the variable manufacturing cost per unit produced? What is the average fixed manufacturing cost per unit produced? (Round your answers to 2 decimal places.)

4. If 27,000 units are produced, what are the total amounts of direct and indirect manufacturing costs incurred to support this level of production?

5. What total incremental manufacturing cost will Hixson incur if it increases production from 25,000 to 25,001 units? (Round your answer to 2 decimal places.)

6. What is Hixson’s contribution margin per unit? What is its contribution margin ratio? (Round "Contribution margin per unit" to 2 decimal places and "Contribution margin ratio" to 1 decimal place.)

7. What is Hixson’s break-even point in unit sales? What is its break-even point in dollar sales? (Do not round your intermediate values.)

8. How much will Hixson’s net operating income increase if it can grow production and sales from 25,000 units to 26,500 units?

9. What is Hixson’s margin of safety at a sales volume of 25,000 units? (Do not round your intermediate values.)

10. What is Hixson’s degree of operating leverage at a sales volume of 25,000 units? (Round your answer to 1 decimal places.)

Please answer all questions:

1)Write the formula for the updating function mt+1 = f(mt) in the following scenario, and then find the solution function mt = f(t). During a particularly dry season, the volume of water in a lake increases by 3% each day from precipitation, and then 8% of the volume of water is removed through a river. On day t0, the lake has 20,000 acre feet of water.

2)Use the solution function from the above example to determine the time it would take under these conditions for the lake’s volume to be reduced by half.

3) Identify the average, amplitude, period, and phase of the following oscillating functions.

(a) g(t) = cos(5(t + π)) − 3.

(b) h(t) = 1 ?8+6cos(2π(2t−1))?

4)The function f(x) has the following properties: f(3) = 5, f(4) = 2, and f′(3) = −2. Write the equations for the secant line of f between x = 3 and x = 4, and the tangent line at x = 3.

5) Identify the critical points and state where the function is increasing and decreasing for the function f(x)=x^3-3x. The find the derivative of f(x) and sketch it

6)Suppose a function f(x) = g(x)/h(x) . Use the following table to calculate f′(3), and write the equation of the tangent line to f at x = 3.

question 1

The following table provides a description for the project Z.

1. What is the critical path of this project?

2. What is the duration of this project? (before crashing)

3. If your task is to crash this project by 2 days, what is the most efficient cost of doing it? (Just input the number with no decimals or dollar signs

question 2

The expected duration of the project (average) is 30 days and variance is 16.

1. What is the probability that the project will be completed on day 32 or earlier?

2. Suppose the official deadline for the project is 34 days. What is the probability that the project will be delayed?

question 3

A restaurant has tracked the number of meals served at lunch over the last four weeks. The data show little in terms of trends, but do display substantial variation by day of the week. Use the following information to determine the seasonal (daily) indices for this restaurant.