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Abstract Algebra : Permutations

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UCLA

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Abstract Algebra : Permutations

HW: Compute lots of commutators [Not just for finite sets]

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Determine a business you could start, algebra homework help

Determine a business you could start, algebra homework help

Task 1
You are starting a new business in which you have decided to sell two products
instead of just one. Determine a business you could start and choose two products
that you could sell. How much of your own money are you willing to invest in this
business in order to get started? How much will each item cost you to make? How
much will you charge for each item?
a. Explain this business (how much of your own money you’re willing to spend
on the business, what items you’re going to sell, costs for each item, sale
price for each item, etc.).
b. Consider the total amount you’re willing to spend on the business and how
much it will cost you to make your items. Write an inequality that represents
the fact that while making each item, you can’t exceed this limit. Be sure to
include the cost per item in this inequality.
c. Graph your inequality. Be sure to label your graph and shade the appropriate
side of the line.
d. Choose a point that falls in the shaded region. Explain what the x-coordinate
and y-coordinate represent and the significance in terms of cost of this point
falling in the shaded region.
e. Choose a point that falls directly on the line. Explain what the x-coordinate
and y-coordinate represent and the significance in terms of cost of this point
falling directly on the line.
f. Choose a point that does not fall in the shaded region. Explain what the xcoordinate
and y-coordinate represent and the significance in terms of cost of
this point falling outside of the shaded region. Task 2
Consider the total amount you’re willing to spend to start your business. After
selling your items, you want your total amount earned to be at least three times
the amount you originally spent.
a. How much money are you hoping to earn from selling your products?
b. Determine the price you want to sell each item for. Note:You may need to
adjust the original prices that you came up with in Task 1.
c. Write an inequality that represents the fact that you want your total earned
to be at least three times the amount that you originally spent. Be sure to
include the price for each item in this inequality.
d. Graph your inequality. Be sure to label your graph and shade the appropriate
side of the line. In the context of the problem, does the shaded area make
sense? If not, make sure to adjust the original values (the investment and
the sale price for both products) so that your shaded area is reasonable.
e. Choose a point that falls in the shaded region for both this inequality and the
inequality you found in Task 1. Explain what the x-coordinate and ycoordinate
represent and the significance in terms of both cost and money
earned of this point falling in the shaded regions.
f. What is the ideal number of items you should produce and sell? Why?
Task 3
Pick one of your items. You have been contacted by a customer in Alaska who
wants to purchase several of these items and wants you to ship the items to her.
You have already established the cost per item and you will only charge the
customer $5 to ship these items to Alaska. Suppose another company sells the
same item but charges half of your price. However, if the customer buys from this
company, she will be charged $20 in shipping costs.
a. Write two equations to represent the customer’s total cost based on how
many items she buys from each of the two sellers—you and the other
company.
b. If the customer in Alaska wants to buy 5 items, from whom should she buy?
Explain your answer.
c. If the customer in Alaska wants to buy 50 items, from whom should she buy?
Explain your answer.
d. Solve the system of equations from part A. What method did you choose to
solve the system? Why?
e. Explain what your solution for part D means in terms of the situation.

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