You are the Deputy Minister, and you are the only one that knows the marginal cost of producing gadgets. Your boss, the Minister of Gadgetry, knows only the demand function, and is completely ignorant about the production side of gadgets. He will believe anything you tell him about the total cost of any project, and will approve a project only if the total benefit of the project $($knowing the demand, he can calculate himself the total benefit$)$ is at least as high as the total cost you claim.

For the project of producing $70$ gadgets, what is the highest cost you can claim and still get approval?

How much bureaucratic slack do you obtain from this project?

What is the project that maximizes your slack? That is$,$ how many gadgets would you propose to produce and what is the total cost you will claim from the Minister?

What is total surplus of this project?