Solve the following mathematical problems:

How many ways are there to divide 50 people into 3 groups so that each group contains members equal to a prime number?

Differentiate financial and economic costs with suitable example. The total revenue (TR) and Average Cost (AC) functions of a firm are given by $$\begin{gathered} TR=4350Q-13Q^2 \\ AC=Q^2-5.5Q +150+675Q^2 \end{gathered}$$ Where Q refers to quantity of output. Find the profit maximizing level of output and maximum profit.

Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

Find the equilibrium output,

Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

What are the tax revenue at equilibrium output? Does the government have a balanced budget?

Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

Find the equilibrium output when investment increases from $70 to $90.

Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

What has happened to the relationship of government spending and tax revenues? Why?