Answer:
The company should not make 300 bicycles.
Step-by-step explanation:
Mathematically speaking, profit ([tex]P(y)[/tex]) equals the difference between revenue ([tex]R(y)[/tex]) and cost ([tex]C(y)[/tex]). That is:
[tex]P(y) = R(y) - C(y)[/tex] (1)
If we know that [tex]R(y) = 2\cdot y^{2}+10\cdot y + 500[/tex] and [tex]C(y) = y^{2}+10\cdot y+100000[/tex], then the profit function is:
[tex]P(y) = 2\cdot y^{2}+10\cdot y +500 -y^{2}-10\cdot y -100000[/tex]
[tex]P(y) = y^{2}-99500[/tex] (2)
The company can make the required amount of bicycles if and only if [tex]P(y) > 0[/tex]. If [tex]y = 300[/tex], then the profit of company is:
[tex]P(300) = 300^{2}-99500[/tex]
[tex]P(300) = -9500[/tex]
The company should not make 300 bicycles.
