Question

The revenue function for a dog food company is modelled by the function R(d) = - 40d^2 + 200d, where d is the price for a can of dog food. The cost function for the production of the dog food is C(d) = 300 – 40d At what price(s) for a can of dog food will the company break even?​

Answer 1

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):

$R(d) = - 40d^2 + 200d\\\\C(d) = 300-40d\\\\\\R(d)=C(d)\\\\-40d^2+200d=300-40d\\\\-40d^2+240d-300=0\\\\\\d=\dfrac{-240\pm\sqrt{240^2-4(-40)(-300)}}{2(-40)}\\\\\\d=\dfrac{-240\pm\sqrt{57600-48000}}{-80}\\\\\\d=\dfrac{-240\pm98}{-80}=3\pm1.225\\\\\\d_1=3+1.225=4.225\\\\d_2=3-1.225=1.775$