1. Suppose that the prices for a 1-year commitment for internet services are $39.99 for standard speed and $49.99 for high speed. For a two-year commitment, these prices are $34.99 and $44.99, respectively. Create a plan price matrix, P, with commitment time along the rows and speed along the columns.a. Suppose prices will go up by $2.00 for standard speed and $3.00 for high speed. Create a prices increase matrix, and perform the necessary arithmetic to show the new prices matrix, N, after the price hikes.
b. Suppose that, after the price hikes, a 3% tax is applied to all prices. Show the operation performed on N to get prices after the tax.
2. Suppose that Matrix A below shows the cost of purchasing a variety of laptops of varying memory sizes, and matrix B shows the number of each size a small company wishes to purchase. Multiply A and B (in order), and describe the real-world meaning of the result.
3. A mixture of water and pure antifreeze will be combined to create a 42% antifreeze mixture. Determine the amount of water and antifreeze needed to produce 1.5 gallons. Do so by defining variables, writing constraints in verbal and equation form, and by then solving using the method of substitution.
4. A plant makes aluminum and copper wire. Each pound of aluminum wire requires 5 kwh of electricity and 1/4 hr. of labor. Each pound of copper wire requires 2 kwh of electricity and 3/4 hr. of labor. Production of copper wire is restricted by the fact that that raw materials are available to produce at most 80 lbs./day. Electricity is limited to 400 kwh/day and labor to 60 person-hrs./day. If the profit from aluminum wire is $.35/lb. and the profit from copper is $.55lb., the desired question to answer is: How much of each should be produced to maximize profit and what is the maximum profit?a. Define the variables clearly.
b. Write all constraints in words.
c. Write all constraints as mathematical inequalities. (You can use the “pi” symbol in the toolbar to enter formatted inequalities)
d. Describe the objective in words and write the objective function.
5. In the 1994-1995 NBA seasons, All-Star basketball player Michael Jordan had his best year when it came to making 3-point shots; he came in at a 50% success rate! Suppose Michael Jordan attempted three 3-point shots in a single game. a. Assuming his success rate in unaffected by other factors, what is the probability that he makes all three shots?
b. Suppose that Michael Jordan actually performs better on 3-point shots as he makes more-and-more of them within a single game. Assuming his 3-point success rate increases by 10% points for each successive shot he attempts, what is the probability that he made all three of them?
6. Suppose Sony sells a warranty on one of its products. They find the probability that a warranty holder files an accidental damage claim is 15%. The probability they file a claim on a battery is 35%. Each warranty holder can only file up to one of each type of claim and files one type independently of another. Developing a table first will prove to be helpful in easily answering both questions. a. What is the probability that a warranty holder makes claim on their warranty? Assuming filing of an accidental damage claim is independent of filing a battery claim. Calculate.
b. Given that we know someone files a battery claim, how likely are they to file an accidental damage claim?
7. A job posting brings in 5 potential candidates for two positions. Anne and Bill are two of those applicants. What is the probability that at least one of them gets the position for the scenario in which both positions are the same? Both different?
8. A college board is to elect two new board members, whose roles are the same. The pool of potential board members contains 30 Republicans and 25 Democrats.a. In how many ways can two candidates be chosen from the entire group?
b. What is the probability that both are Republican?
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