Algebra word problem

Question

Suppose you have decided to open your own at home business. Your business involves providing physical products to your customers. Before you open for business, you need to first find a shipping company to use. You have narrowed your search down to two shipping companies.

• Hasty Punctual Dispatch charges a base rate of $3 plus $2.5 per pound of the package(s) shipped.

• Nimble Trustworthy Transport charges a base rate of $5 plus $1.50 per pound of the package(s) shipped.

If TC is the total shipping cost and W is the weight shipped:

Hasty Punctual: TC = 3 + 2.5 * W

Nimble Trustworthy: TC = 5 + 1.5* W

Use the equation for each shipping company to create a table of ordered-pair solutions for each shipping company.

Answer 1

This type of problem appears to be leading to the selection of service providers based upon cost. One way to maximize profits is to lower costs.

You can identify the cross-over point where one supplier begins to cost more than another by graphing the functions and looking at the intersection point.

In this case, both cost functions are linear and they intersect at x=2. If the weight of the product you wish to ship is less than two pounds, Hasty has a lower cost. If the weight is more than 2 pounds, Nimble has a lower cost.

Of course, there may be other factors that need to be considered: service from the company, travel distance to the company if they don't pick up for free, etc.

Answer 2