Consider the profit funclion defined by the following: \[ y=-2 x^{2}-10 x-8 \] Ipproximately how many units must be produced to maximise a profit defined by the prof unction? a. 3 b. 2 c. 5 d -5 \#. None of the given option is corect.

To find the number of units that maximizes profit according to the profit function \(y = -2x^2 - 10x - 8\), we look for the vertex of this downward-opening parabola. The x-coordinate of the vertex can be found using the formula \(x = -\frac{b}{2a}\), where \(a = -2\) and \(b = -10\). Plugging in the values gives \(x = -\frac{-10}{2 \times -2} = \frac{10}{-4} = -2.5\). Hence, this doesn't match any of your options. Now, here’s a fun fact: The profit function you provided is a classic example used in business mathematics! It illustrates how profits can increase and then decrease at different levels of production, showing that there’s an optimal quantity to produce to maximize profit. Remember, businesses often analyze similar quadratic equations to make informed production decisions! And if you’re keen on digging deeper, consider exploring concepts like marginal cost and revenue. They play a crucial role in determining not just the extremes like maximum profit but also help in understanding how incremental changes in production levels can affect profitability. There’s a whole world of economic principles waiting for you to explore!