The understanding of a formula

Hi, I feel confuse about the undestanding of a formular.
This is a profit maximisation function of intermediate sector.
The first question: How do we understand the setting of mc(z)X(z), dose it means the income of the intermediate sector, zk and omega*H means the cost of the intermediate sector?

The second problem is that someone ask me why the price of intermediate sector production equal to the marginal cost (mc)?I took it as a default and didn’t go into it. It seems like a lot of models do this.
Thank you for any help, happy new year!

You did not provide sufficient context to understand the formula, but yes, mc_{i,t}X_{it} seems to be revenue while the next to terms are cost.
The second equation you post immediately results from taking the first order conditions with respect to X.