Final answer:
The linear cost function is C(x) = 180x + 1000, where x represents the number of units produced.
Step-by-step explanation:
To find the linear cost function, we need to determine the relationship between the number of units produced and the total cost. In this case, the fixed cost is $1000, which means it remains constant regardless of the number of units produced. Additionally, we are given that 34 units cost $7120. We can use this information to calculate the variable cost per unit.
Variable cost per unit = (Total cost - Fixed cost) / Number of units = ($7120 - $1000) / 34 = $180
Therefore, the linear cost function is: C(x) = 180x + 1000