Grade 11 U math
posted by Jamie .
A 135kg steer gains 3.5kg/day and costs 80 cents/day to keep. The market price for beef cattle is $1.65/kg, but the price falls by 1 cent/day. When should the steer be sold to maximize profit?
Revenue= (Price/units)(#of units)
Cost=(cost/unit)(# of units) + set costs
Profit= RevenueExpenses.
show the revenue and costs.
put in vertex form.

x=days
135kg +3.5kg/day*x =weight
SalePrice= $(1.650.01*x)/kg*weight
cost= $0.8/day*x
profit=Salepricecost
profit(x)=(1.650.01x)(135 +3.5x)0.8x
profit(x)= 1.65*135+1.65*3.5x0.01*135x0.01*3.5x^20.8x
= 222.750+4.4250x0.035x^20.8x
= 222.750+3.625x0.035x^2
set the derivative to 0 to find max profit
dprofit(x)/dx=0
3.6250.07x=0
x=3.625/0.07
x=51.7857~=52
hope this helps
Respond to this Question
Similar Questions

maximizing profit calculus
During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the necklaces for $10 each and his sales averaged 20 per day. When he increased the price by $1, he found that he lost two sales per day. a. … 
COLLEAGE ALEGEBRA
QUES # 1 a STARTUP COMPUTER CAN SELL 1000 COMPUTERS IF THEY PRICE THEM AT $500. tHE NUMBER SOLD WILL INCREASE BY 10 FOR EVERY $1 decrease in the price. The company has fixed costs of $100,999, and each computer costs $300 to produce, … 
math
during the summer months, sarah makes and sells necklaces on the beach. last summer she sold the nacklaces for $10 each. Her sales averaged 20 per day. Considering a price increase, she took a small survey and found that for every … 
CalculusAlmost figured out
Sports store is having a closing down sale, all stock has to be sold. each day an article remains unsold, the price is discounted by 4% of the previous days price. This discounting continues until the article is sold. The table shows … 
math
On first day you receive 1 cent on the second day 2 cents on the third day you get 4 cents and so on for 28 days. How much would you expect to receive on the last day of the month ? 
math
miss Thao owns a small hotel with 30 identical rooms. she finds that if she charges a price of 12 dollars ( or less) per room per day, all the rooms are rented. for every 1 dollar in price, 2 rooms remain vacant. each day, maintenance … 
Math (quadratic function)
A fuel station sell, aproximately, 2140 liters of gasoline, per day, in which each liters costs 1,75 dollars. The owner observed that, reducing the price of the liter, occurs an increase in the volume of fuel sold, in the proportion … 
Calculus
When selling lemonade for 50 cents per cup, Diana can sell 40 cups per day. She observes that the number of cups sold per day decreases by 2 for every 5cent increase in the price of a cup of lemonade. Determine a formula for the number … 
Algebra
A squash patch currently has 120 lbs of butternut squash. For each additional day in the patch, the amount of butternut squash increases by 6 lbs. If the price of butternut squash is currently 80 cents per pound, but it decreases by … 
calc
A farmer has a herd of 100 cattle with an average weight of 500 lbs/cow. It costs 50 cents a day to keep each cattle. They are gaining weight at a rate of 6 lbs per day. The market price is now $1 per lb for beef and is falling by …