Consider the supply equation where x is the quantity supplied in units of a thousand and p is the unit price in dollars.
p=x^3+x+10
Determine the price at which the supplier will make 2,500 units of the commodity available in the market. (Give your answer correct to the nearest cent.)
$ ?
To determine the price at which the supplier will make 2,500 units of the commodity available in the market, we need to solve the supply equation for the given quantity. In this case, we want to find the price (p) when the quantity (x) is 2,500.
The supply equation is:
p = x^3 + x + 10
Now, substitute x = 2,500 into the equation:
p = (2,500)^3 + 2,500 + 10
Using a calculator, calculate the value of (2,500)^3:
p = 15,625,000,000 + 2,500 + 10
Simplifying:
p = 15,625,002,510
Therefore, the price at which the supplier will make 2,500 units of the commodity available in the market is approximately $15,625,002,510.
Please note that the price is given in dollars, and we rounded to the nearest cent.