Kathy and Mark Smith believe investing in their retirement is critical. Kathy began investing 20% of each paycheck in a retirement account when she was 20 years old. She has saved four times more than Mark who began saving when he was 35. If their total retirement savings equals $1,455,000, how much are Kathy's and Mark's investments worth? Kathy's retirement savings Mark's retirement savings

Kathy and Mark Smith believe investing in their retirement is critical. Kathy began investing 20% of each paycheck in a retirement account when she was 20 years old. She has saved four times more than Mark who began saving when he was 35. If their total retirement savings equals $1,455,000, how much are Kathy's and Mark's investments worth? Kathy's retirement savings Mark's retirement savings

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...

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If during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.
Flowering plant species can be subject to inbreeding, through self-fertilization. Some species have adaptations that help to avoid this inbreeding, through asymmetric flower structures. If the flower structures are “right-handed”, then a pollinator visiting the right-handed flower will get pollen on its left side, and thus, only be able to deposit the pollen on a left-handed flower that it visits later on. [Similarly, pollinator visits to left-handed plants will result in pollen deposits on right-handed plants.] You are interested in studying a particular plant species called Lupinus perennis, that demonstrates handedness, and you wish to know whether one type of handedness is more prevalent than the other (e.g., are left-handed plants more prevalent than right-handed plants?) You sample 30 L. perennis plants, and find that 20 plants are right-handed, and 10 plants are left-handed. Is one type of handedness more prevalent than the other? What is your null hypothesis? Report the…
In laparoscopic surgery, a video camera and several thin instruments are inserted into the patient's abdominal cavity. The surgeon uses the image from the video camera positioned inside the patient's body to perform the procedure by manipulating the instruments that have been insert ed. The Top Gun Laparoscopic Skills and Suturing Program was developed to help surgeons develop the skill set necessary for laparoscopic surgery. Because of the similarity in many of the skills involved in video games and laparoscopic surgery, it was hypothesized that surgeons with greater prior video game experience might acquire the skills required in laparoscopic surgery more easily. Thirty-three surgeons partici pated in the study and were classified into the three categories, never used, under three hours, and more than three hours depending on the daily number of hours they played video games at the height of their video game use. They also performed Top Gun drills and received a score based on the…
A wireless carrier offers the following plans that a person is considering. The Family Plan: $ 95 monthly fee, unlimited talk and text on up to 5 lines, and data charges of $ 47 for each device for up to 2 GB of data per device. The Mobile Share Plan: $ 180 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $ 30 for each device up to a shared total of 10 GB of data. Use P for the number of devices that need data plans as part of their cost. Find the model of the total cost of the Family Plan $ Find the model of the total cost of the Mobile Share
Five friends, all of whom are experienced bakers, form a company that will make bread and cakes and sell them to local restaurants and specialty stores. Each loaf of bread requires 50 minutes of labor and ingredients costing $0.90 and can be sold for $1.80 profit. Each cake requires 30 minutes of labor and ingredients costing $1.50 and can be sold for $3.00 profit. The partners agree that no one will work more than 8 hours a day. Their financial resources do not allow them to spend more than $190 per day on ingredients. How many loaves of bread and how many cakes should they make each day to maximize their profit?
Donna De Paul is raising money for the homeless. She discovers that each church group requires 2 hours of letter writing and 1 hour of follow-up, while for each labor union she needs 2 hours of letter writing and 3 hours of follow-up. Donna can raise $125 from each church group and $200 from each union local, and she has a maximum of hours 20 of letter writing and a maximum of 12 hours of follow-up available per month. Determine the most profitable mixture of groups she should contact and the most money she can raise in a month. Let x1 be the number of church groups, and let x2 be the number of labor unions. What is the objective function? z= ___x1 + ____x2 Do not include the $ in your answer
Donna De Paul is raising money for the homeless. She discovers that each church group requires 2 hours of letter writing and 1 hour of follow-up, while for each labor union she needs 2 hours of letter writing and 3 hours of follow-up. Donna can raise $125 from each church group and $175 from each union local, and she has a maximum of hours 20 of letter writing and a maximum of 12 hours of follow-up available per month. Determine the most profitable mixture of groups she should contact and the most money she can raise in a month. Let be the number of church groups, and let be the number of labor unions. What is the objective function?
A fund-raising company is putting together a student kit of candy bars for a school to use in its annual support campaign. To maximize sales, the company will put more of the most popular candy bar sold in an average day in each kit. The company’s research shows that of the five most popular candies, local vending machines sell 100 of Candy A, 14 of Candy B, 50 of Candy C, 6 of Candy D, and 45 of Candy E on an average day. Which candy on average is the most popular candy? Which averaging method did you use?
The government is auctioning off oil leases at two sites. At each site, 150,000 acres of land are to be auctioned. Cliff Ewing, Blake Barnes, and Alexis Pickens are bidding for the oil. Government rules state that no bidder can receive more than 45% of the land being auctioned. Cliff has bid $2000 per acre for site 1 land and $1000 per acre for site 2 land. Blake has bid $1800 per acre for site 1 land and $1500 per acre for site 2 land. Alexis has bid $1900 per acre for site 1 land and $1300 per acre for site 2 land. a. Determine how to maximize the government’s revenue with a transportation model. b. Use SolverTable to see how changes in the government’s rule on 45% of all land being auctioned affect the optimal revenue. Why can the optimal revenue not decrease if this percentage required increases? Why can the optimal revenue not increase if this percentage required decreases?
The Gem City Paper Company produces rolls of paper of various types for its customers. One type is produced in standard rolls that are 50 inches wide and 100 yards long. Customers of this type of paper order rolls that are 100 yards long but can have any of the widths 12, 15, 25, 30, and 40 inches. In a given week, Gem City Paper waits for all orders and then decides how to cut its 50-inch rolls to satisfy the orders. The weekly number of orders for each roll width is provided in the table below. Each week this company must decide how to cut its rolls in the most economical way to meet its orders. Specifically, it wants to produce and cut as few rolls as possible. Formulate and solve an IP model to help Gem City Paper find the best way to meet all weekly customer demands. (Hint: list all the feasible patterns that can be used to cut a 50-inch roll of paper). Width 12 15 25 30 40 Requirement 40 30 20 20 20
An archery target consists of a gold circle with radius of 5 inches surrounded by a red ring whose diameter is 20 inches. Next, there are three progressively larger rings – blue, black, and white. The diameter of each ring is 10 inches larger than the diameter of the previous ring. John is a beginner so his aim is poor and, if his arrow hits the target, its location on the target is completely at random. John shoots and then yells, “I hit it!” Without using your calculator, find the following probabilities. Write the answers as a percentage. a) The probability his arrow landed in the gold circle is ______. b) The probability his arrow landed in the white area is ______. c) The probability his arrow landed in the red or the blue area is ______.