Question 394851
{{{graph(300, 300, 0, 20, 0, 20, 5x^(-1/2), x^(4/5))}}}


This question does not make sense. The green curve shows the cost of production, for producing q units. However, the red curve is a demand curve, and demand curves show how prices change with demand. In other words, it has to show the price per unit with a demand of q. The two curves have different y-axes (price per unit and total cost) and they cannot be easily combined in any way.


In any economic market, I don't think p(q) would represent the profit because there is an asymptote at q = 0 (i.e. maximum profit occurs when there is zero production).


It is fairly likely that p(q) is the price for a unit(however it would not be a demand curve, it would be a supply curve since it models supply, q, over price). If this is so, then the profit is most likely explained as {{{y = q*p(q) - c(q) - 2}}}. You can work from there on, taking the derivative of y in terms of q just like the other tutor did. However this may not be true since q is the amount *supplied*, and not necessarily the amount actually sold.


If the two graphs are legitimate supply and demand curves (that is, the red curve shows how price is affected by demand, and the green curve shows how price is affected by supply), then the optimal profit usually occurs at equilibrium, where the demand and supply are equal. Then you can set p(q) = c(q) and solve.


Or, p(q) shows the demand with a given supply q. However, this makes the question unsolvable, as the y-axes of the green and red curves show the total cost and the amount demanded (also note that it is the amount demanded, not the amount actually sold).