Taylor Polynomial, Interval and Radius of Convergence and General Binomial Theorem

Please see the attached file for the fully formatted problems.

Bill owns a bike company, and wants to know how many bicycles and tricycles he should manufacture, with no leftovers, and how many boxes of seats he will order. (details given in actual problem)

Bill runs Bill's Big Bikes, a company that manufactures bicycles and specialty adult-sized tricycles. The bicycles and tricycles use the same-sized wheels and identical seats. Right now, Bill has 68 wheels in the shop and needs to order seats. Unfortunately, the company that supplies the seats will only ship seats in boxes of 6. Bill does not want to order more wheels and does not want to order more seats than he needs. How many bicycles and tricycles should be manufactured to use all of the wheels Bill has in stock and all of the seats that he will ultimately order? How many boxes of seats will he order? I only know how to sove this by 'trial and error', and by that I came up with t... click for more

An investor has $60,000 to invest in a CD and mutual fund. How much should be invested in CD's, and how much in the mutual fund to maximize return? This is a linear programming problem on investing

For the following linear programing problem, define variables, write the objective function, and all constraints. Then solve the problem. An investor has $60,000 to invest in a CD and a mutual fund. The CD yields 5%, and the mutual fund yields 9%. The mutual fund requires a minnimum investment of $10,000, and the investor requires that exactly twice as much should be invested in CD's as in the mutual fund. How much should be invested in CD's and how much in the mutual fund to maximize the return? What is the maximum return?

Probability Question

Tom and Jim decided to play the following game for points. A single die is rolled. If it shows a non-prime number, Tom receives points equal to two times the number of dots showing. If it shows a prime number, Tom loses points equal to three times the number of dots showing. What is the expected value of the game?

Probability Quesion

In order to test a new car, an automobile manufacturer wants to select 4 employees to test drive the car for one year. If 12 management and 8 union employees volunteer to be test drivers and the selection is made at random, what is the probability that at least one union employee is selected?