Question: [#10 from page 171 (instructor modified)]. A manufacturer plans to use either Robot " A " or

Robot " B " in one of its new production processes. Robot " A " costs $180,000 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 5,000

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 ≤ 5 ,000 ).

1. [ 2 ] Write the total COST function C = f ( x ) for each Robot.
2. [ 2 ] At what number of hours "x" would the total COSTs of using either Robot be
   the same?
3. [ 2 ] Calculate each Robot’s total COSTs at the value of " x " from part "b".
4. [ 2 ] Which of the two Robots would COST the least to operate for 4,567 hours
   during a particular production cycle? What is this COST?
5. [ 4 ] Use the Chart Wizard feature of Excel to graph each of the two alternatives.
   Base your two data points on total COST @ x = 0 hours and @ x = 5,000 hours.
   Then use a trend line to represent each set of data points, and indicate each trend
   line’s equation.
6. [ 2 ] For what values of " x " will the least costly alternative be Robot " A "? Robot
   " B "?
7. [ 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 $260,000 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.

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