Question

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.
i Equation for your company: Click or tap here to enter text.
ii Equation for other company: Click or tap here to enter text.
b. If the customer in Alaska wants to buy 5 items, from whom should she buy? Explain your answer.
i Click or tap here to enter text.
c. If the customer in Alaska wants to buy 50 items, from whom should she buy? Explain your answer.
i Click or tap here to enter text.
d. Solve the system of equations from part A.
i Click or tap here to enter text.
b What method did you choose to solve the system?
i Click or tap here to enter text.
e. Explain what your solution for part D means in terms of the situation.
i Click or tap here to enter text.

Answer 1

[AI-generated answer — Bot GPT 3.5]

a.

i. Equation for your company: Total cost = 5(number of items) + 5 (shipping cost)
ii. Equation for other company: Total cost = 0.5(cost per item)(number of items) + 20 (shipping cost)

b. If the customer in Alaska wants to buy 5 items, she should buy from your company because your total cost for 5 items is $30 ($25 for items + $5 for shipping), while the other company's total cost is $22.50 ($12.50 for items + $20 for shipping).

c. If the customer in Alaska wants to buy 50 items, she should buy from the other company because their total cost for 50 items is $45 ($25 for items + $20 for shipping), while your company's total cost is $255 ($250 for items + $5 for shipping).

d. Solving the system of equations:
5n + 5 = 0.5n + 20
4.5n = 15
n = 15/4.5
n = 3.33

The customer should buy 4 items (as you cannot buy a fraction of an item) from your company to have a lower total cost.

e. The solution for part D means that the customer should buy 4 items from your company to have the lowest total cost for her purchase, as buying from the other company would result in a higher overall cost even though their cost per item is lower.