Answer:
The breakeven prices are d_1=4.225 and d_2=1.775.
Step-by-step explanation:
The break even point represents the point in which the profit is zero. In other words, where the revenue equals the cost.
We have functions that describe both the revenue and the cost. The brackeven price is such that R(d)=C(d):
[tex]R(d) = - 40d^2 + 200d\\\\C(d) = 300-40d\\\\\\R(d)=C(d)\\\\-40d^2+200d=300-40d\\\\-40d^2+240d-300=0\\\\\\d=\dfrac{-240\pm\sqrt{240^2-4(-40)(-300)}}{2(-40)}\\\\\\d=\dfrac{-240\pm\sqrt{57600-48000}}{-80}\\\\\\d=\dfrac{-240\pm98}{-80}=3\pm1.225\\\\\\d_1=3+1.225=4.225\\\\d_2=3-1.225=1.775[/tex]
