A cow weighing 300 pounds gains 8 pounds per day, and costs $0.60 a day to keep.

Question

A cow weighing 300 pounds gains 8 pounds per day, and costs $0.60 a day to keep. The market price for beef is $0.75 per pound, but is felling $0.01 per day. When should the cow be sold to maximize profit? A paint manufacturer has a uniform annual demand for 16,000 cans of automobile primer. It costs $4 to store one can of paint for one year and $500 to set up the plant for production of the primer. How many times a year should the company produce this primer in order to minimize the total storage and setup costs?

Explanation / Answer

4.

The weight of the cow, after "x" days will be 300+ 8x pounds.

The market value will be (.75 - .01x) dollars

$ .6 a day goes in keeping the cow

So the profit function is P(x) = (300 + 8x)(.75 - .01x) - .6x

for maximum profit find the critical point

for that find P '(x) = 2.4 - .16x

P '(x) = 0

=> x = 15

now maximum profit is = P(x= 15) = $ 243

hence the cow should be sold on the 15 th day from the start.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.