Question

The willingness of manufacturers of aluminum baseball bats to produce bats depends on the price that the bats will sell for This relationship can be modeled by S(p)=0.12p² −4.6p+55 where S(p) represents the supply of bats in millions when p is the price in dollars and the price is greater than $20.

a) The manufacturors are willing to supply _____ million bats when the price is $31.

Answer 1

When the price is $31, the manufacturers are willing to supply 27.72 million aluminum baseball bats, calculated using the supply function S(p) = 0.12p² - 4.6p + 55.

Step-by-step explanation:

The relationship between the price of aluminum baseball bats and the willingness of manufacturers to produce them can be represented by the supply function S(p) = 0.12p² − 4.6p + 55. Here, S(p) represents the supply of bats in millions when p is the price in dollars. To find out how many million bats manufacturers are willing to supply when the price is $31, we simply plug the price into the function:

1. Let p = 31.
2. Plug p into the supply function: S(31) = 0.12∙31² − 4.6∙31 + 55.
3. Perform the calculations: S(31) = 0.12∙961 − 142.6 + 55.
4. The calculation results in: S(31) = 115.32 − 142.6 + 55.
5. Finally, S(31) = 27.72 million bats.

Therefore, the manufacturers are willing to supply 27.72 million bats when the price is $31.