# math

posted by ibranian

Your company can make x-hundred grade A tires and y-hundred grade B tires a day, where 0≤x≤4 and y= (40-10x)/(5-x). The profit on each grade A tire is twice the profit on each grade B tire. Assuming all tires sell, what are the most profitable numbers of tire to make?

1. Reiny

Profit = 2(x) + 1(40-10x)/(5-x)
= 2x + (40-10x)/(5-x)
= (2x^2 - 40)/(x-5)
d(profit)/dx = [(x-5)(4x) - (2x^2 - 40)(1) ]/(x-5)^2
= 0 for a max of profit

4x^2 - 20x - 2x^2 + 40 = 0

x^2 - 10x + 20 = 0
x = 5 ± √5
= appr 7.24 or appr 2.76
but x must be between 0 and 4, so x = 2.76
where x is in hundreds

so for a max profit they should make 276 A tires
and 552 B tires

check my arithmetic,

2. lamar henderson

(3,0),(-2,6),(1,5),(3,6)

## Similar Questions

1. ### Physics

I have to compare and contrast three types of tires, and relate them to physics. I've chosen: <li> Racing tires <li> Winter tires <li> All season tires I've chosen to compare them on: <li> Tire tread pattern …
2. ### Statistics

A purchasing agent for a trucking company is shopping for replacement tires for their trucks from two suppliers. The suppliers' prices are the same. However, Supplier A's tires have an average life of 60,000 miles with a standard deviation …
3. ### Statistics

A purchasing agent for a trucking company is shopping for replacement tires for their trucks from two suppliers. The suppliers' prices are the same. However, Supplier A's tires have an average life of 60,000 miles with a standard deviation …
4. ### statistics

Assume that Acme Tires sells their high performance tires for \$180 each and their all weather tires for \$135 each. Further assume that the cost of producing a high performance tire is \$150 and the cost of producing an all weather tire …
5. ### Calculus

P(x)= -x^3+15x^2-48x+450, x>/3 is an approximation to the total profit (in thousands of dollars) from the sale of x hundred thousand tires. find the number of hundred thousands of tires that must be sold to maximize profit.

Rocky Mountain Tire Center sells 20,000 go cart tires per year. The ordering cost for each tire is \$40, and the holding cost is 20% of the purchase price of the tires per year. The purchase price is \$20 per tire if fewer than 500 tires …
7. ### math

A company has two factories that manufacture tires. Suppose 65% of the tires are manufactured in factory 1 and 35% are manufactured in factory 2. In factory 1, 5% of the tires are defective. In factory 2, 2% of the tires are defective. …
8. ### math

20. A tire company manufactures 50 tires an hour with its current staff. The company can make 10 extra tires per hour for every extra worker it hires. Which of the following equations represents this relationship mathematically, with …
9. ### math

A tire company determines that to manufacture a certain type of tire, it costs \$9000 to set up the production process. Each tire that is produced costs \$21 in material and labor. The company sells this tire to wholesale distributors …
10. ### math

A tire company manufactures 50 tires an hour with its current staff. The company can make 10 extra tires per hour for every extra worker it hires. Which of the following equations represents this relationship mathematically, with x …

More Similar Questions