A manufacturer will purchase either Robot “A” or Robot “B” to use in a new
production processes. Robot “A” costs $170,000 and has estimated hourly operational
costs of $100; Robot “B” costs $250,000 and has estimated hourly operational costs of
$80. Assume conditions are such that 6,000 represents the maximum number of hours
“x” that either Robot might be utilized during any production cycle (i.e. the restricted
“domain” for this problem is 0 x 6,000).
1. [2] Which of the two Robots would COST the least to operate for 3,456 hours
2. [6] Use the Chart feature of Excel to graph each of the two alternatives, using two
data points. Base your two points on total COST @ x = 0 hours and @ x = 6,000
hours. Then use a linear trend line to represent each set of data points, and indicate
each trend line’s equation.
3. [4] For what “x” values will the least costly alternative be Robot “A”? Robot “B”?
4. [2] After completing the above computations for Robots “A” and “B”—but prior to
purchasing either Robot—one of your associates discovers that a third Robot—
Robot “C” is available. It costs $275,000 and has estimated operational costs of
$110 per hour. Write the total COST function C = f(x) for Robot “C”. Then,
determine for what values of “x” Robot “C” would be the least costly alternative.
production processes. Robot “A” costs $170,000 and has estimated hourly operational
costs of $100; Robot “B” costs $250,000 and has estimated hourly operational costs of
$80. Assume conditions are such that 6,000 represents the maximum number of hours
“x” that either Robot might be utilized during any production cycle (i.e. the restricted
“domain” for this problem is 0 x 6,000).
1. [2] Which of the two Robots would COST the least to operate for 3,456 hours
2. [6] Use the Chart feature of Excel to graph each of the two alternatives, using two
data points. Base your two points on total COST @ x = 0 hours and @ x = 6,000
hours. Then use a linear trend line to represent each set of data points, and indicate
each trend line’s equation.
3. [4] For what “x” values will the least costly alternative be Robot “A”? Robot “B”?
4. [2] After completing the above computations for Robots “A” and “B”—but prior to
purchasing either Robot—one of your associates discovers that a third Robot—
Robot “C” is available. It costs $275,000 and has estimated operational costs of
$110 per hour. Write the total COST function C = f(x) for Robot “C”. Then,
determine for what values of “x” Robot “C” would be the least costly alternative.