A manufacturer produces widgets with both variable and fixed daily costs. The total daily cost C (in dollars) for producing n widgets is given by a linear function.
If the total cost for producing 50 widgets is $550 and the total cost for producing 80 widgets is $790, what is the fixed daily cost?
- $150 (correct answer)
- $200
- $250
- $300
Explanation: Let the linear cost function be C = an + b where a is the cost per unit and b is the fixed cost. We have two points: (50, 550) and (80, 790). The slope is a = (790 - 550)/(80 - 50) = 240/30 = 8. Using point-slope form with (50, 550): C - 550 = 8(n - 50), so C = 8n - 400 + 550 = 8n + 150. Therefore, the fixed daily cost is $150. Choice B results from incorrectly calculating the slope. Choice C comes from slope calculation errors. Choice D results from errors in the point-slope calculation.