To solve the problem, you are given the equation for profit:

$\text{profit} = 17.54x - 10171.9$

where $x$ represents the number of units produced. You're asked to find the profit when $x = 146.5$ units.

Steps to solve:

1. Substitute $x = 146.5$ into the profit equation: $\text{profit} = 17.54(146.5) - 10171.9$

2. Perform the multiplication: $17.54 \times 146.5 = 2569.51$

3. Subtract the constant value: $2569.51 - 10171.9 = -7602.39$

Final Answer:

The profit when producing 146.5 units is -7602.39.

Although it seems unusual to have a negative profit, this simply means the costs have exceeded the revenue at this level of production.

Would you like further details, or do you have any additional questions?

Follow-up questions:

1. What does a negative profit indicate in a business context?
2. How would the profit change if more units were produced, say 200 units?
3. Can you interpret the meaning of the constants 17.54 and -10171.9 in the profit equation?
4. What is the break-even point, where profit equals zero, in this case?
5. How would you model profit if there were variable costs involved?

Tip:

If the profit is negative, the company may need to either reduce costs or increase the selling price to become profitable.