What is the Optimal Number of Birdhouses to Produce?

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In summary, Tom expects to sell at least 30 birdhouses a week at $60 each, but if he produces more than 30, he will lose $2 per additional house. The ideal number of houses to produce would be the point at which the revenue function, C(x) = (30 + x)(60 - 2x), is optimized.
  • #1
abbarajum
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Hi everyone - this is my second post on here today!

Anyway, I have a word problem, and would just like to make sure I am setting it up correctly.

Tom expects to sell at least 30 birdhouses a week, at \$60 each. If he produces more than 30, he will lose \$2 per additional house. What is the ideal number of houses to produce?

I have an idea of how to set it up, but just want to make sure it is correct.

I have the equation as: C(x) = (30 + x)(60 - 2x)

Would this be correct to use in this case? The number of total houses to produce would be 30 + x, and the price per house would be 60 - 2x. Is my reasoning correct?

Thanks in advance!
 
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  • #2
Yes, your revenue function $C(x)$ looks good to me. You have expressed the total revenue as the product of the number of units produced and the revenue per unit. (Yes)

Can you proceed to optimize the revenue function?

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