Hi, can you help me with detailed explanations on questions below Thank you Problem 1 You are the marketing manager of a firm that produces Titanium and sells this metal to two distinct kinds of customers aircraft producers and golf club manufacturers Demand for Titanium by these two market segments is quite different, as described by the respective price equations PA 10 QA 600 and PG 12 QG 100, where annual quantities are in thousands of pounds and prices are in dollars Your firm estimates the marginal cost of titanium production at $4 per pound a) What is the optimal price and quantity for the aircraft segment b) What is the optimal price and quantity for the golf segment c) Because of Titanium shortages, the firm's total production capacity drops to only 1 5 million pounds per year Determine the firm's optimal quantities in this case Problem 2 Gold Trackers monitors the price of precious metals, and has daily data on prices and sales of gold for the past several years One of their new MBA financial wizards has estimated the following relationship for gold sales in the past year of trading (250 observations) Q 4000 0 01 P 1 5 I 1 25 X 2 0 S (857) (0 002) (0 65) (0 44) (0 48) R 2 0 96 Where Q daily sale of gold in ounces, P is the price of gold in dollars per ounce, I is the most recent one month report on US CPI inflation (in percent), X is an index on the exchange rate of the US dollar compared to seven other currencies, and S is the market price of an ounce of silver in dollars Standard errors are in parentheses a) Evaluate the results of this regression Compute t statistics and F statistic b) Recently the price of gold has been $380 per ounce, inflation was measured at 0 2 for the month, the dollar has been trading at 99 7 on the foreign exchange index, and silver has been steady at $4 75 per ounce What is the expected quantity of gold that will trade on a daily basis c) Are gold and silver substitutes or complements Explain Problem 3 In early 2002, Mrs Smyth's, a Chicago based food company, initiated an empirical estimation of demand for its gourmet frozen fruit pies The firm wants to formulate pricing and promotional plans for the future on the basis of historical data, and management is interested in learning how pricing and promotional decisions might affect sales Mrs Smyth's has been marketing frozen fruit pies for several years, and its market research department has collected quarterly data over two years for six important marketing areas, including unit sales quantity, the retail price charged for the pies, local advertising and promotional expenditures, and the price charged by a major competing brand of frozen pies Statistical data published by the U S Census Bureau on population and disposable income in each of the six market areas were also available for analysis It was therefore possible to include a wide range of hypothesized demand determinants in an empirical estimation of fruit pie demand Year Quarter Unit Sales ( Q ) Price ($) Advertising Expenditures ($) Competitors' Price ($) Income ($) Population Time Variable ( T ) Atlanta, GA 2000 1 193,334 6 39 15,827 6 92 33,337 4,116,250 1 2000 2 170,041 7 21 20,819 4 84 33,390 4,140,338 2 2000 3 247,709 5 75 14,062 5 28 33,599 4,218,965 3 2000 4 183,259 6 75 16,973 6 17 33,797 4,226,070 4 2001 1 282,118 6 36 18,815 6 36 33,879 4,278,912 5 2001 2 203,396 5 98 14,176 4 88 34,186 4,359,442 6 2001 3 167,447 6 64 17,030 5 22 35,691 4,363,494 7 2001 4 361,667 5 30 14,456 5 80 35,950 4,380,084 8 Chicago, IL, 2000 1 401,805 6 08 27,183 4 99 34,983 9,184,926 1 Gary, IN, 2000 2 412,312 6 13 27,572 6 13 35,804 9,237,683 2 Kenosha, WI 2000 3 321,972 7 24 34,367 5 82 35,898 9,254,182 3 2000 4 445,236 6 08 26,895 6 05 36,113 9,272,758 4 2001 1 479,713 6 40 30,539 5 37 36,252 9,300,401 5 2001 2 459,379 6 00 26,679 4 86 36,449 9,322,168 6 2001 3 444,040 5 96 26,607 5 29 37,327 9,323,331 7 2001 4 376,046 7 21 32,760 4 89 37,841 9,348,725 8 Dallas Fort 2000 1 255,203 6 55 19,880 6 97 34,870 5,294,645 1 Worth, TX 2000 2 270,881 6 11 19,151 6 25 35,464 5,335,816 2 2000 3 330,271 5 62 15,743 6 03 35,972 5,386,134 3 2000 4 313,485 6 06 17,512 5 08 36,843 5,409,350 4 2001 1 311,500 5 83 16,984 5 29 37,573 5,409,358 5 2001 2 370,780 5 38 15,698 6 19 37,781 5,425,001 6 2001 3 152,338 7 41 22,057 6 94 37,854 5,429,300 7 2001 4 320,804 6 19 17,460 6 38 39,231 5,442,595 8 Los Angeles 2000 1 738,760 5 75 42,925 5 54 28,579 16,381,600 1 Long Beach, CA 2000 2 707,015 6 61 50,299 6 73 28,593 16,544,289 2 2000 3 699,051 5 03 37,364 5 04 28,633 16,547,258 3 2000 4 628,838 6 76 50,602 4 61 28,833 16,553,958 4 2001 1 631,934 7 04 53,562 5 85 29,242 16,587,432 5 2001 2 651,162 6 70 48,911 5 63 29,876 16,680,782 6 2001 3 765,124 6 54 49,422 6 94 30,327 16,716,936 7 2001 4 741,364 5 73 44,061 6 37 30,411 16,717,938 8 Minneapolis 2000 1 291,773 5 35 13,896 5 78 29,778 2,972,443 1 St Paul, MN 2000 2 153,018 6 33 27,429 4 73 30,079 2,974,275 2 2000 3 574,486 5 94 31,631 6 70 30,598 2,989,720 3 2000 4 75,396 7 00 39,176 4 58 30,718 3,020,244 4 2001 1 590,190 5 19 33,538 5 17 30,922 3,021,618 5 2001 2 288,112 7 02 53,643 5 15 31,199 3,025,298 6 2001 3 276,619 7 02 60,284 5 46 31,354 3,042,834 7 2001 4 522,446 5 23 53,595 6 06 31,422 3,063,011 8 Washington, DC, 2000 1 395,314 5 80 22,626 6 56 38,892 7,611,304 1 Baltimore, MD 2000 2 436,103 5 32 22,697 6 38 39,080 7,615,783 2 2000 3 336,338 6 35 25,475 4 53 39,510 7,666,220 3 2000 4 451,321 5 95 25,734 6 31 39,552 7,710,368 4 2001 1 352,181 6 01 23,777 6 24 39,776 7,713,007 5 2001 2 317,322 7 02 27,544 4 86 41,068 7,752,393 6 2001 3 422,455 5 71 23,852 4 86 47,471 7,754,204 7 2001 4 290,963 7 36 30,487 5 32 41,989 7,782,654 8 Average 391,917 6 24 29,204 5 70 34,625 7,706,365 A linear regression of the following form was run Qit b0 b1Pit b2Ait b3 PXit b4Yit b5Popit b6Tit The subscript i indicates the regional market from which the observation was taken, whereas the subscript t represents the quarter during which the observation occurred Where Q is the quantity of pies sold during the t th quarter P is the retail price in dollars of Mrs Smyth's frozen pies A represents the dollars spent on advertising PX is the price, measured in dollars, charged for competing fruit pies Y is dollars of disposable income per capita Pop is the population of the market area T is a trend factor (2000 1 1, , 2001 4 8) Source SS df MS Number of obs 48 F (6, 41) 58 86 Model 1 30E 12 6 2 17E 11 Prob F 0 Residual 1 51E 11 41 3 68E 09 R squared 0 896 Adj R squared 0 8808 Total 1 45E 12 47 3 09E 10 Root MSE 60699 O Coef Std Err P t 95 Conf Interval Const 646825 8 151790 9 4 26 0 000 340277 8 953373 7 P 127358 3 14918 85 8 54 0 000 157487 5 97229 03 A 5 351046 1 081889 4 95 0 000 3 166126 7 535966 PX 29403 91 12405 93 2 37 0 023 4349 628 54458 19 Y 0 324286 2 854491 0 11 0 910 5 440474 6 089047 Pop 0 023962 0 0023508 10 19 0 000 0 0192149 0 02871 T 4395 644 4398 263 0 323 4486 828 13278 12

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Hi, can you help me with detailed explanations on questions below: Thank you! Problem # 1 You are the marketing manager of a firm that

Hi, can you help me with detailed explanations on questions below:

Thank you!

Problem # 1 You are the marketing manager of a firm that produces Titanium and sells this metal to two distinct kinds of customers: aircraft producers and golf club manufacturers. Demand for Titanium by these two market segments is quite different, as described by the respective price equations: PA = 10 - QA./600 and PG = 12 - QG./100, where annual quantities are in thousands of pounds and prices are in dollars. Your firm estimates the marginal cost of titanium production at $4 per pound. a) What is the optimal price and quantity for the aircraft segment? b) What is the optimal price and quantity for the golf segment? c) Because of Titanium shortages, the firm's total production capacity drops to only 1.5 million pounds per year. Determine the firm's optimal quantities in this case.

Problem # 2 Gold Trackers monitors the price of precious metals, and has daily data on prices and sales of gold for the past several years. One of their new MBA financial wizards has estimated the following relationship for gold sales in the past year of trading (250 observations): Q = 4000 - 0.01 P + 1.5 I - 1.25 X + 2.0 S (857) (0.002) (0.65) (0.44) (0.48) R 2= 0.96 Where Q = daily sale of gold in ounces, P is the price of gold in dollars per ounce, I is the most recent one-month report on US CPI inflation (in percent), X is an index on the exchange rate of the US dollar compared to seven other currencies, and S is the market price of an ounce of silver in dollars. Standard errors are in parentheses. a) Evaluate the results of this regression. Compute t-statistics and F-statistic. b) Recently the price of gold has been $380 per ounce, inflation was measured at 0.2% for the month, the dollar has been trading at 99.7 on the foreign exchange index, and silver has been steady at $4.75 per ounce. What is the expected quantity of gold that will trade on a daily basis? c) Are gold and silver substitutes or complements? Explain.

Problem # 3 In early 2002, Mrs. Smyth's, a Chicago based food company, initiated an empirical estimation of demand for its gourmet frozen fruit pies. The firm wants to formulate pricing and promotional plans for the future on the basis of historical data, and management is interested in learning how pricing and promotional decisions might affect sales. Mrs. Smyth's has been marketing frozen fruit pies for several years, and its market research department has collected quarterly data over two years for six important marketing areas, including unit sales quantity, the retail price charged for the pies, local advertising and promotional expenditures, and the price charged by a major competing brand of frozen pies. Statistical data published by the U.S. Census Bureau on population and disposable income in each of the six market areas were also available for analysis. It was therefore possible to include a wide range of hypothesized demand determinants in an empirical estimation of fruit pie demand.

	Year-Quarter	Unit Sales (Q)	Price ($)	Advertising Expenditures ($)	Competitors' Price ($)	Income ($)	Population	Time Variable (T)
Atlanta, GA	2000-1	193,334	6.39	15,827	6.92	33,337	4,116,250	1
	2000-2	170,041	7.21	20,819	4.84	33,390	4,140,338	2
	2000-3	247,709	5.75	14,062	5.28	33,599	4,218,965	3
	2000-4	183,259	6.75	16,973	6.17	33,797	4,226,070	4
	2001-1	282,118	6.36	18,815	6.36	33,879	4,278,912	5
	2001-2	203,396	5.98	14,176	4.88	34,186	4,359,442	6
	2001-3	167,447	6.64	17,030	5.22	35,691	4,363,494	7
	2001-4	361,667	5.30	14,456	5.80	35,950	4,380,084	8

Chicago, IL,	2000-1	401,805	6.08	27,183	4.99	34,983	9,184,926	1
Gary, IN,	2000-2	412,312	6.13	27,572	6.13	35,804	9,237,683	2
Kenosha, WI	2000-3	321,972	7.24	34,367	5.82	35,898	9,254,182	3
	2000-4	445,236	6.08	26,895	6.05	36,113	9,272,758	4
	2001-1	479,713	6.40	30,539	5.37	36,252	9,300,401	5
	2001-2	459,379	6.00	26,679	4.86	36,449	9,322,168	6
	2001-3	444,040	5.96	26,607	5.29	37,327	9,323,331	7
	2001-4	376,046	7.21	32,760	4.89	37,841	9,348,725	8

Dallas-Fort	2000-1	255,203	6.55	19,880	6.97	34,870	5,294,645	1
Worth, TX	2000-2	270,881	6.11	19,151	6.25	35,464	5,335,816	2
	2000-3	330,271	5.62	15,743	6.03	35,972	5,386,134	3
	2000-4	313,485	6.06	17,512	5.08	36,843	5,409,350	4
	2001-1	311,500	5.83	16,984	5.29	37,573	5,409,358	5
	2001-2	370,780	5.38	15,698	6.19	37,781	5,425,001	6
	2001-3	152,338	7.41	22,057	6.94	37,854	5,429,300	7
	2001-4	320,804	6.19	17,460	6.38	39,231	5,442,595	8

Los Angeles-	2000-1	738,760	5.75	42,925	5.54	28,579	16,381,600	1
Long Beach, CA	2000-2	707,015	6.61	50,299	6.73	28,593	16,544,289	2
	2000-3	699,051	5.03	37,364	5.04	28,633	16,547,258	3
	2000-4	628,838	6.76	50,602	4.61	28,833	16,553,958	4
	2001-1	631,934	7.04	53,562	5.85	29,242	16,587,432	5
	2001-2	651,162	6.70	48,911	5.63	29,876	16,680,782	6
	2001-3	765,124	6.54	49,422	6.94	30,327	16,716,936	7
	2001-4	741,364	5.73	44,061	6.37	30,411	16,717,938	8

Minneapolis-	2000-1	291,773	5.35	13,896	5.78	29,778	2,972,443	1
St. Paul, MN	2000-2	153,018	6.33	27,429	4.73	30,079	2,974,275	2
	2000-3	574,486	5.94	31,631	6.70	30,598	2,989,720	3
	2000-4	75,396	7.00	39,176	4.58	30,718	3,020,244	4
	2001-1	590,190	5.19	33,538	5.17	30,922	3,021,618	5
	2001-2	288,112	7.02	53,643	5.15	31,199	3,025,298	6
	2001-3	276,619	7.02	60,284	5.46	31,354	3,042,834	7
	2001-4	522,446	5.23	53,595	6.06	31,422	3,063,011	8

Washington, DC,	2000-1	395,314	5.80	22,626	6.56	38,892	7,611,304	1
Baltimore, MD	2000-2	436,103	5.32	22,697	6.38	39,080	7,615,783	2
	2000-3	336,338	6.35	25,475	4.53	39,510	7,666,220	3
	2000-4	451,321	5.95	25,734	6.31	39,552	7,710,368	4
	2001-1	352,181	6.01	23,777	6.24	39,776	7,713,007	5
	2001-2	317,322	7.02	27,544	4.86	41,068	7,752,393	6
	2001-3	422,455	5.71	23,852	4.86	47,471	7,754,204	7
	2001-4	290,963	7.36	30,487	5.32	41,989	7,782,654	8

Average		391,917	6.24	29,204	5.70	34,625	7,706,365

A linear regression of the following form was run: Qit = b0 + b1Pit + b2Ait + b3 PXit + b4Yit + b5Popit+b6Tit The subscript i indicates the regional market from which the observation was taken, whereas the subscript t represents the quarter during which the observation occurred. Where Q is the quantity of pies sold during the t-th quarter P is the retail price in dollars of Mrs. Smyth's frozen pies A represents the dollars spent on advertising PX is the price, measured in dollars, charged for competing fruit pies Y is dollars of disposable income per capita Pop is the population of the market area T is a trend factor (2000 - 1= 1, ....., 2001 - 4 = 8)

Source SS df MS Number of obs = 48 F (6, 41) = 58.86 Model 1.30E + 12 6 2.17E + 11 Prob > F = 0 Residual | 1.51E + 11 41 3.68E + 09 R-squared = 0.896 Adj R-squared = 0.8808 Total | 1.45E + 12 47 3.09E + 10 Root MSE = 60699 O | Coef. Std.Err. P>|t| [95% Conf. Interval] Const | 646825.8 151790.9 4.26 0.000 340277.8 953373.7 P -127358.3 14918.85 -8.54 0.000 -157487.5 -97229.03 A 5.351046 1.081889 4.95 0.000 3.166126 7.535966 PX 29403.91 12405.93 2.37 0.023 4349.628 54458.19 Y 0.324286 2.854491 0.11 0.910 -5.440474 6.089047 Pop 0.023962 0.0023508 10.19 0.000 0.0192149 0.02871 T 4395.644 4398.263 0.323 -4486.828 13278.12