A company needs to package 2,400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container
can hold 80 pencils. Each box costs the company $0.50, while each cylindrical container costs $0.75. Which packaging should the company use to minimize cost? Explain.
If the company used rectangular prisms it would take 40 boxes (2400/60) to hold 2,400 pencils which would cost $20 (40 times 0.50). If they used cylindrical containers, they would need 30 containers (2400/80) for a total of $22.50 (30*0.75).
To minimize the cost the company should go with rectangular prisms as they are the most cost effective.
For this case the first thing we must observe is that the mass increases 0.4 grams when the diameter increases 1 millimeter. Therefore, the slope of the line is given by: m = 0.4 Thus, the function that best suits the table is given by: f (x) = -4 + 0.4x For example, for x = 20 we have: f (20) = -4 + 0.4 (20) f (20) = -4 + 8 f (20) = 4 The result, matches the table. Answer: The function that is best represented by the scatter plot is: f (x) = -4 + 0.4x
