The understanding of a formula

General DSGE Modeling
1

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?

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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.
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Thank you for any help, happy new year!

2

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.