Everyone's favorite type of math question, word problems
After working on these for a few hours and getting nowhere! I even tried having my brother help me . I would appreciate any and all help with the following word problems that will be the death of me ():
1. (Buying and selling beef.) A steer weighing 300 pounds gains 8 pounds per day and costs 1.00 dollar a day to keep. You bought this steer today at a market price of 1.50 dollars per pound. However, the market price is falling 2 cents per pound per day. When should you sell the steer in order to maximize your proﬁt?
2. (Maximizing production.) An orange grower in California hires migrant workers to pick oranges during the season. He has 12 employees, and each can pick 400 oranges per hour. He has discovered that if he adds more workers, the production per worker decreases due to lack of supervision. When x new workers (above the 12) are hired, each worker picks
400 − 2x 2 oranges per hour.
(a) Write the total number N (x) of oranges picked per hour as a function of x;
(b) Find the domain of N (x);
(c) Graph the function N (x);
(d) Estimate the maximum number of oranges that can be picked per hour;
(e) Find the number of employees involved in part (d).
3. (Biology.) The volume V of a lung is directly proportional to its internal surface area A. A lung with volume 400 cm3 from a certain species has an average internal surface area of 100 cm2 . Find the volume of a lung of a member of this species if the lung’s internal surface area is 120 cm2 .
Thank you math gurus out there!