Please show all work

Show all work please Suppose that you have estimated the market demand and supply in the price taking industry in whic your firm operates and have obtained: Qd= 25,000-5000P+25M Qs=240,000+5,000P-2,000PI Where P is price, M is income, and is the price of a key input. You also anticipate that incomes in the relevant market next year will be $15,000 and the price of the input will be $20. Additionally, Average variable cost is estimated to be : AVC= 14-0.008Q+0.000002Q2 & Total fixed cost will be $6,000 next year. a. Find the market price forecast for next year. b. Find the output that will maximize profits given your forecast for market price. Explain why you chose this answer. c. Calculate profits at this output. Graph both the market graph and the graph of the firm right next to it. Be sure to make the connection between what is going on in the market graph and the graph of the firm. Label both axes on your market graph. Label the numerical value for price on the graph of the firm, also label the numerical value of ATC, and the numerical value for firm quantity on the graph. Depict the profit/loss box. d. Now suppose that income is expected to drop to $10,000, with no other changes to the market supply function, AVC function or FC. What would be the new profit maximizing output? What would be profits? Do you advise this firm to produce at this new output or to shut down? Explain your answer with numbers and also draw in a new graph of the market and firm. Be sure to label the numerical value for price on the graph of the firm, also label the numerical value of ATC, and the numerical value for firm quantity on the graph. Depict the profit/loss box