A farmer has 360 acres of land on which to plant corn and wheat. She has $24,000 in resources to use for planting and tending the fields and storage facility sufficient to hold 18,000 bushels of the grain (in any combination). From past experience, she knows that it costs $120 / acre to grow corn and $60 / acre to grow wheat; also, the yield for the grain is 100 bushels / acre for corn and 40 bushels / acre for wheat. If the market price is $225 per acre for corn and $100 per acre for wheat, how many acres of each crop should she plant in order to maximize her revenue?
1. Set up a linear programming problem, choosing variables, finding a formula for your objective function, and inequalities to represent the constraints.
2. You will need to decide a reasonable range for your variables, and then put in a column of values within that range for the x-variable in column A. Then you want to solve each constraint equation for y, and use that formula to get values in the "y for C1", etc., columns (B, C, D). Then graph the three constraint lines on one graph (as you did in Lab 1: open its Word document if you need refreshing on how to do this).
3. Shade in the feasible region.
4. Find the corners of the feasible region using goal seek to find intersections of lines, as you did in Lab 1.
5. Find in column H the values of f at the corners of the feasible region.
6. Determine the maximum revenue.
7. Finally, using new objective functions for when the prices of corn are at their highs and lows, answer the final question. This only involves computing new values of the objective function, not any new graphing or constraints.
Formula for objective function: f =
Corners of feasible region f at corners
So how many acres of each crop should she plant?
Formulate a system of equations for the situation below and
A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve, and long-sleeve. The time (in minutes) required by each department to produce a dozen blouses of each type is shown in the following table.
The cutting, sewing, and packaging departments have available a maximum of 87, 176, and 52 labor-hours, respectively, per day. How many dozens of each type of blouse can be produced each day if the plant is operated at full capacity?
Chapter 3.6, Problem 20E in Introduction to Linear Algebra (5th Edition)
Find the basis for the null space and the range of the given matrix. Then use Gram-Schmidt to obtain the orthagonal bases.
Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.
You need a $80,000 loan.
Option 1: a 30-year loan at an APR of 7.15%
Option 2: a 15-year loan at an APR of 6.75%
Find the monthly payment for each option.
The monthly payment for option 1 is $___
The monthly payment for option 2 is $___
Find the total amount paid for each option.
The total payment for option 1 is $_____
The total payment for option 2 is $___(Use the answers from the previous step. Round to the nearest cent as needed.)
Prove that R>2r. R is circumradius and r is inradius of a triangle.
Derive Heron's formula.
g. Now let’s say you wait just 5 years before you start saving for retirement, how much will that cost you in interest? How about 10 years? How about just 1 year? (10 points) Now you need to consider if that is enough. If you live to be 90 years old, well above average, then from the time you retire, to the time you are 90, you will have to live on what you have in retirement (not including social security). So if you retired at 65, you will have another 25 years where your retirement funds have to last. h. Determine how much you will have to live on each year. Note, we are neither taking into account taxes nor inflation (which is about 2% a year). (5 points) Let’s look at this from the other direction then, supposing that you wanted to have $50,000 a year after retirement. i. How much would you need to have accumulated before retirement? (5 points) j. How much would you need to start investing each year, beginning right now, to accumulate this amount? A “short-cut” to doing this is to first compute the effective yield at your retirement age, then divide this amount into Part (i). This is the amount you well need to invest each year. (5 points) k. That was just using $50,000, how much would you want to have each year to live on? Dream big or reasonable depending on your occupation! Now using that value, repeat parts (i) and (j) again. You need to state what you would want to live on and it needs to be something besides $50,000. (10 points) Your answer to (k) would work, if you withdrew all of your retirement funds at once and divided it up. However, if you left the money in the account and let it draw interest, it is possible that the interest itself would be enough to live on, or at the very least if you had to withdraw some of the principle, the remaining portion would still continue to earn interest. Essentially, what you have found is the upper bound for the amount of money that you will need to invest each year to attain your financial goals. l. Finish by summarizing what you have learned in the entire project and consider setting a goal towards saving for retirement. (Your answer should be in complete sentences free of grammar, spelling, and punctuation mistakes.) This should be a paragraph not one sentence. (10 points)
1.38.4. The diagonal of a parallelogram and segments from any point on the diagonal to the vertices through which the diagonal does not pass divide the parallelogram into two pairs of equal triangles.
A. 271 and 516
1. Find the greatest common divisor, d, of the two numbers from part A using the Euclidean algorithm. Show and explain all work.
2. Find all solutions for the congruence ax ? d
(mod b) where a and b are the integers from
part A and d is the greatest common divisor from part A1.
Show and explain all work.
Construct the 2 × 2 matrix for the linear transformations R 2 → R 2 defined by the following compositions. In each case, write down the matrix of each transformation, then multiply the matrices in the correct order.
(a) A dilation by a factor of 4, then a reflection across the x-axis.
(b) A counterclockwise rotation through π/2 , then a dilation by a factor of 1/2 .
(c) A reflection about the line x = y, then a rotation though an angle of π.
Please write a few sentences on the following two topics:
1. The system of coordinates is a "bridge" between algebra and geometry. Why? How? Etc....
2. Relations between straight lines and linear equations.
Please write neatly, and in detail. Thank you so much!
A $1000 par value 4% bond with semiannual coupons matures at the end of 10 years. The bond is callable at $1050 at the ends of years 4 through 6, at $1025 at the ends of years 7 through 9, and at $1000 at the end of year 10. Find the maximum price that an investor can pay and still be certain of a yield rate of 5% convertible semiannually.
1. Discuss the different properties of Matrices for each matrix
2. What is the importance of interface in fiber reinforce composite?
The Oregon Atlantic company produces two types of paper:
newsprint and wrapping paper. Make 1 yard of newspaper
It takes 5 minutes to produce one yard of newspaper; and 8 minutes to make one yard of wrapping paper. The company has 4,800 hours of operation per week. Newspapers cost $ 0.20 per yard and wrapping paper yields $ 0.25 per yard. Demand per week is 500 yards for newspaper and 400 yards for wrapping paper. sales price need labour hour is 1 hour.The company has established the following goals in order of importance:
(1) Limit overtime to 480 hours or less.
(2) Create a profit of $ 300 per week.
(3) profit size.
(4) Do not make fun of production capacity.
a. Determining how many different types of paper should be
produced to satisfy various goals
Formulate it as a goal planning method model.
b. Use your computer to solve the problem.
1) How much will you have accumulated over a period of 30 years if, in an IRA which has a 10% interest rate compounded quarterly, you annually invest:
a. $1 b. $4000 c. $10,000 d. Part (a) is called the effective yield of an account. How could Part (a) be used to determine Parts (b) and (c)? (Your answer should be in complete sentences free of grammar, spelling, and punctuation mistakes.)
2) How much will you have accumulated, if you annually invest $1,500 into an IRA at 8% interest compounded monthly for: a. 5 year b. 20 years c. 40 years d. How long will it take to earn your first million dollars? Your answer should be exact rounded within 2 decimal places. Please use logarithms to solve.