Manufacturing—Average Costs: Consider the following data table for the cost and revenues at various production levels for a new brand of computer printer.
Number of printers produced, x | Cost, C(x) | Revenue, R(x) |
1000 | 243,600 | 296,950 |
2000 | 363,000 | 575,800 |
3000 | 482,800 | 818,550 |
4000 | 603,300 | 1,007,200 |
(a) Use your calculator to determine a linear regression model for the cost of producing the printer in the form
C(x) = ax + b 1 ≤ x ≤ 4
where x represents the number of printers produced in thousands and C(x) represents the cost of production.
(b) Use your calculator to determine a cubic regression model for the revenue of producing and selling the printers in the formR(x) = ax3 + bx2 + cx + d 1 ≤ x ≤ 4
where x represents the number of printers produced and sold in thousands and R(x) represents the resulting revenue.
(c) Compute MAC(x) and simplify the result.
(d) Evaluate MAC(1.5) and interpret.
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