What is the Optimal Number of Birdhouses to Produce?

  • Context: MHB 
  • Thread starter Thread starter abbarajum
  • Start date Start date
  • Tags Tags
    Word problem
Click For Summary
SUMMARY

The optimal number of birdhouses to produce is determined by the revenue function C(x) = (30 + x)(60 - 2x), where Tom expects to sell at least 30 birdhouses weekly at a price of $60 each. Producing more than 30 birdhouses incurs a loss of $2 for each additional unit. The discussion confirms that the setup of the revenue function is correct and invites further optimization of this function to maximize profit.

PREREQUISITES
  • Understanding of revenue functions and optimization techniques
  • Basic algebra for manipulating equations
  • Familiarity with profit-loss scenarios in production
  • Knowledge of how to derive and analyze functions
NEXT STEPS
  • Learn how to derive revenue functions from production scenarios
  • Study optimization techniques in calculus, specifically for maximizing functions
  • Explore profit-loss analysis in production economics
  • Investigate the impact of pricing strategies on sales volume
USEFUL FOR

Entrepreneurs, business analysts, and anyone involved in production planning or pricing strategy will benefit from this discussion.

abbarajum
Messages
5
Reaction score
0
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!
 
Physics news on Phys.org
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?

Note: If you wish to use dollar signs in your posts as dollar signs rather than $\LaTeX$ tags, precede them with a backslash:

\$
 

Similar threads

MHB Expected number of sold books and profit
  • · Replies 5 ·
Replies
5
Views
1K
MHB What is the average profit on producing and selling 40 items per day
  • · Replies 1 ·
Replies
1
Views
2K
MHB Real Estate math word problem help
  • · Replies 3 ·
Replies
3
Views
2K
MHB Win a $10 or $5 Prize in Tom's 4/19 Lottery Fundraiser
  • · Replies 1 ·
Replies
1
Views
2K
High School Two interesting number theory tricks
  • · Replies 3 ·
Replies
3
Views
1K
MHB with Cost,Volumn,Profit and Trade Discount
  • · Replies 2 ·
Replies
2
Views
4K
MHB Help with Profit/Loss: Find Optimal Number of Items to Buy
  • · Replies 1 ·
Replies
1
Views
2K
MHB Why Do Different Calculations of a Probability Problem Yield Different Results?
  • · Replies 1 ·
Replies
1
Views
3K
MHB Determine the best price for a amusement ride
  • · Replies 1 ·
Replies
1
Views
2K
MHB Probability: twice the same number
  • · Replies 10 ·
Replies
10
Views
2K