Hi, I need help with my Econo homework

1. A company has an inverse demand function p = 8 - 0.004Q, and a total cost function TC = Q + 0.006Q2. (p is in dollars, and Q is in thousands of units).

(1) What is the optimal price p* and quantity Q* to maximize its profit?

(2) Graph the marginal revenue function and marginal cost function in the (Q, p) space. What is the slope of each curve? Indicate the intercept of each endpoint in the graph. Indicate the optimal Q* and p* in the graph.

(3) What is the point elasticity of demand at (Q*, p*)? Rounding to two decimal places.

(4) Suppose now the company adopts a more efficient technology and the cost of producing each the additional unit reduces by 50 cents. What is the new marginal cost function? What is the new optimal price and quantity, i.e., Q*new and p*new? (Hint: the marginal cost reduces by 0.5 dollars).

(5) Graph the new marginal cost function in the same graph of (2). Indicate the direction of any movement or shift of the marginal cost function in the graph. Indicate Q*new and p*new.

(6) Given the new technology, what is the point elasticity of demand at (Q*new, p*new)? Compared with (3), is it more or less elastic? Rounding to two decimal places.