I'm having trouble on my homework and I need some help. A company sells products in a perfectly competitive market, where the price is $p = 24.$ For each of the following cost functions, write down the company’s profit-maximization problem, and then find $q^∗$.
i. $C(q) = 2q^3$
ii. $C(q)=30q+q^2$
iii. $C(q) = 10q$
iv. $C(q) = 24q$
I finished i and ii on my own, for i, $$\max_q \text{Total Revenue}-\text{Total Cost} = \max_q 24q-2q^3,$$ then I take the derivative of max, I get $24-6(q^*)^2$ and set it equal to 0, I get $q^*=2$ and $q^*=-2$, then use the second-order condition find out $q^*=2$. For ii, I get $q^*=-3$. But for iii, I get $$24q-10q=14q,$$ when I take derivative I get $14$, how can I set $14=0$? What is $q^*4$ in this situation? Or does $q^*$ even exist? Also for iv, the FOC is $0=0$, what is $q^*$ in this situation? Any help would be appreciated.