Sample Math 111 Applications Final

Sample Math 111 Applications final

Name______

First section:

1) A contractor charges $35 to come out to a job sight. In addition the contractor charges $22.50 an hour for the work done at the sight. Write a linear function that models the expense of this contractor in terms of the number of hours worked. Use this model to find the expense to have the contractor do 6 hours of work.

2) You have 350 feet of fencing to enclose a rectangular plot that boarders a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is that area?

3) Prehistoric cave paintings were discovered in a cave in France. The paint contained 25% of its original carbon-14. Given the half life of Carbon-14 as 5715 years, estimate the age of the painting.

Second section:

4) A bird species recoveringfrom the brink of extinction has a population that is increasing exponentially. Seven years ago the population was 435 and today there are 1240 of the birds in the wild. How long will it take the population to recover to its pre-1995 population levels of 7500 wild birds?

5) At a college production of A Music Man, 510 tickets were sold. The ticket prices were $8, $10, and $12, and the total income from ticket sales was $6200. How many tickets were sold of each type if the combined number of $8 and $10 tickets sold was 5 times that of the number of $12 tickets sold?

SET UP BUT DO NOT SOLVE A SYSTEM OF EQUATIONS THAT WOULD PROVIDE THE ANSWER REQUESTED.

6) A theater is presenting a program on drug abuse for parents and children. Admission is $2.00 for parents and $1.00 for children. However the theater can only hold 150 people. Furthermore for each two parents there must be at least one child. Set up an objective function and a system of constraint equations that would find the maximum money that could be raised in terms of the number of children and parents in attendance.

Third Section:

7) Federal express wants to purchase larger aircraft. They have the option to buy up to 20 Boeing 727’s and as many Falcon 20s as they may need. Each Boeing 727cost $1400 per hour to operate and carries 42,000 pounds. Each Falcon 20 costs $500 per hour to operate but only carries 6000 pounds of payload. Federal Express needs to carry at least 672,000 pounds of payload and only wants to spend up to $35,000 per hour in operation costs. How many of each type of plane should be purchased in order to maximize the number of aircraft they will have?

8) A Semi-Elliptical tunnel is 18 feet high and 46 feet wide. How far from the edge of the tunnel can a road be placed while leaving a 14.5 foot clearance for vehicles passing underneath?

9) At a science museum you find a pair of curved walls facing each other 100 feet apart. Placed between these walls are two podiums, each 6 feet from the surface of the corresponding wall. Standing at one podium you are able to have a conversation with a person at the other podium as if you are standing next to one other. The person on the other podium asks “How is this possible?” In answer to their question write the equation of the conic section from which the curved walls are formed.