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.
a. Let x represent the number of items the customer wants to buy.
For your company:
Total cost = (cost per item * x) + 5
For the other company:
Total cost = (half of your price * x) + 20
b. Let's compare the two options when the customer wants to buy 5 items:
For your company:
Total cost = (cost per item * 5) + 5
For the other company:
Total cost = (half of your price * 5) + 20
You need to compare these two total costs and see which one is lower.
c. Let's compare the two options when the customer wants to buy 50 items:
For your company:
Total cost = (cost per item * 50) + 5
For the other company:
Total cost = (half of your price * 50) + 20
Again, you need to compare these two total costs and see which one is lower.
d. To solve the system of equations, I would substitute the expressions for total cost in terms of x from part a into the equation from part a.
For your company:
(cost per item * x) + 5 = (half of your price * x) + 20
Simplify the equation and solve for x.
e. The solution for part d (the value of x) will tell us the number of items the customer should buy from each company in order to minimize the total cost. The solution will indicate how many items the customer should buy from each company to make it more cost-effective.