A. It's confusing to have both C(x) and C as a value.
Clearly it is possible to have P(x) = R(x) - C(x) that has no maximum.
For example, if both are linear functions.
B. Of course. P(x) is continuous, so it must have a maximum value on a closed interval, even if it is constant. That would be the maximum (and also minimum) value.
C. of course not. See A above
1. Suppose C(x) is a function representing the cost (in dollars) of producing x units of energy, and R(x) is a function representing the revenue (in dollars) of selling x units of energy. Suppose further that both functions are continuous for all x > = 0.
A. Is there necessarily some x value, let's call it C, that will maximize profit over all x > = 0? Explain your answer.
B. Suppose we know we can't produce more than 1,000 units of energy. Is there necessarily some x-value, call it C, that will maximize profit over the interval [0,1000]? Explain your answer.
C. Again, assume that we can't produce more than 1,000 units of energy. Is there necessarily some x value, let's call it C, for which the profit is exactly 0? Explain your answer
2 answers
Thank you so much this really helped me!!!!