I just need help with G and H.A through F have already been completed. NAME Megan Schuyler (2) Due 12/3/2022 Show work for credit!The demand for product Q is given by Q = 220-P and the total cost of Q by:STC =1000 +80Q -3Q² ++0²aFind the price function and then the TR function. See Assignment 3 or 4 for anexample.Q=220-PP=220-QTR=(PIQTR = (220 – 0J0TR=220Q - Q²b. Write the MR and MC functions below. Remember: MR = gTB/dQ and MC =OSTC/dQ. See Assignment 5 for a review of derivatives.dTR= 220Q - Q²(2200) = 220(1)Q¹-¹ = 220(Q²) = 2(Q²-¹) = 2QdQdTRdQdTRdQMR = 220 - 20PROFIT ANALYSISdTCdo (1000) = 0dQdTC(800) = 80(3Q²) = 3(2)Q²-¹ = 6Q(²0²) = (3) 0²-¹ = Q²dQdTCdodTCMC = 80 - 6Q+Q²c. What positive value of Q will maximize total profit? Remember: setting MR = MCand solving for Q will give you the Q that maximizes total profit. The value of Q youget should not be zero or negative.MR = MC220 20 80 - 6Q+Q²Q²6Q +20 + 80-220 = 0Q²4Q-140 = 0Q(Q14) +10(Q14) = 0(Q + 10) (Q14) = 0Q10 or Q = 14Value of Q that maximizes profit would equal 14d. Use the price function found in (a) to determine the price per unit that will need tobe charged at the Q found in (c). This will be the price you should ask per unit foreach unit of Q that maximizes total profit.P = 220 - QP220 14PROFIT ANALYSISP = 206A price of 206 should be charged for each unit of Q that maximizesprofit.e. How much total profit will result from selling the quantity found in (c) at the pricefound in (d)? Remember: profit is TR-STC.TR = 206(14) = 2884 total revenueSTC = 1000 + 80Q-3Q² +0³STC = 1000 + 80(14) — 3(14)² + (14)²1STC = 1000 + 1120-3(196) +(2744)STC = 2120588 +914.67STC = 2446.67Profit = TR - STCProfit = 2884 - 2446.67Maxiumum Profit = 437.33f. At what level of Q is revenue maximized? Remember, let MR = 0 and solve for Q.MR = 0 signals the objective of maximizing revenue.Total revenue maximizes when MR = 0.TR = 220Q - Q²dTRMR =dQMR 220 2QMR = 0220-2Q=0220 = 2QPROFIT ANALYSIS220Q=2Q = 110When Q=110 it will maximize the total revenueg. At what positive level of Q is marginal profit maximized? You found the profitfunction in (e) above. Marginal profit is the first derivative of the profit function (e).Next, find the derivative of marginal profit, set it equal to zero, and solve for Q. Thisis the Q that maximizes marginal profit.h. What price per unit should be charged for each unit of Q found in (g)? Simply plugthe Q you got in (g) into the same price function you found in (a) and also used in(d).Profit2.doc 5-20-21

TR(Total revenue )is the amount that the seller earns by selling their product.TC(Total cost )is the…

NAME Megan Schuyler (2) Due 12/3/2022 Show work for credit! The demand for product Q is given by Q-220-P and the total cost of Q by: STC-1000+800-3Q¹ +² a. Find the price function and then the TR function. See Assignment 3 or 4 for an example Q-220-P P-220-Q TR-(PQ TR-(220-0 TR=2200- Q b. Write the MR and MC functions below. Remember: MR-TB/dQ and MC- 4STC/40, See Assignment 5 for a review of derivatives. dTR -=220Q- Q² (2200) 220(1)Q-220 dQ dTR dQ dTR do (0²)2(0-¹)=2Q dQ MR=220-20 dTC dQ dTC dQ PROFIT ANALYSIS dQ dTC dQ MC (1000) = 0 (800)=80 (3Q²) = 3(2)Q²-¹6Q (₁²) = (3)0²-²=Q² 80-60+0² c. What positive value of Q will maximize total profit? Remember: setting MR-MC and solving for Q will give you the Q that maximizes total profit. The value of a you get should not be zero or negative. MRMC 220-20 80-6Q+Q² Q²-60+20+80-220 = 0 Q-40-140=0 Q(Q-14)+10(Q-14)=0 (Q+10)(Q-14)=0 Q-10 or Q=14 Value of Q that maximizes profit would equal 14 PROFIT ANALYSIS d. Use the price function found in (a) to determine the price per unit that will need to be charged at the Q found in (c). This will be the price you should ask per unit for each unit of Q that maximizes total profit. P = 220 - Q 14 P= 220 P = 206 A price of 206 should be charged for each unit of Q that maximizes profit. e. How much total profit will result from selling the quantity found in (c) at the price found in (d)? Remember: profit is TR-STC. TR= 206(14) = 2884 total revenue STC= 1000+80Q-3Q² +0² STC= 1000+80(14)-3(14)²+(14)² STC=1000+1120-3(196) +(2744) STC=2120-588 +914.67 STC= 2446.67 Profit= TR-STC Profit=2884-2446.67 Maxiumum Profit=437.33 f. At what level of Q is revenue maximized? Remember, let MR-O and solve for Q MR-0 signals the objective of maximizing revenue. Total revenue maximizes when MR = 0. TR=220Q-Q dTR dQ MR = MR = 220-2Q MR=0 220-20 0 220- 20 PROFIT ANALYSIS 220 Q=110 When Q=110 it will maximize the total revenue At what positive level of Q is marginal profit maximized? You found the profit function in (e) above. Marginal profit is the first derivative of the profit function (e). Next, find the derivative of marginal profit, set it equal to zero, and solve for Q. This is the Q that maximizes marginal profit. h. What price per unit should be charged for each unit of Q found in (g)? Simply plug the Qyou got in (g) into the same price function you found in (a) and also used in (d). Profit2.doc 5-20-21