PART I: 1st/2nd/3rd Order Models Background In PART I of Problem Set 1, you found yourself the hypothetical manager of product line Red10. Based on data for the past 12 sales periods associating this product line's units sold \"x\" and total PROFIT \"P\" results for the sales periods, you used Excel's Chart feature to (1) graph a plot of the data, (2) add the most appropriate 1st and 2nd order \"trend lines\" and trend line equations and (3) identify each trend line's coefficient of determination [(R2)]. You also used the spreadsheet calculator provided in Module 1 to calculate the adjusted [(R2)adj] value for the 2nd order model. Finally, having recently become knowledgeable about 3rd order models, you use Excel's Chart feature and the Module 1 adjusted [(R2)adj] calculator to develop 3rd order model information. Your summary graph is provided on the next page, and provides the starting point for developing solutions for the items in Sections A, B and C on page 3. Product Red10 Units [x] 20 40 80 160 220 320 380 420 520 Profit [P] 640 770 835 -588140 -568960 -510560 -327040 -146140 199360 411940 547860 839360 102944 0 924985 711785 2nd Order R-Sq (Adj) Calculato r 1 Chart (R^2) = 0.9595 k= 2 n= 12 (n-1) = 11 (n-(k+1)) = 9 1-(R^2) = 0.0405 adj. R^2= 0.9505 3rd R-Sq (Adj) Chart (R^2) = Order Calculato r 1 k= 3 n= 12 (n-1) = 11 (n-(k+1)) = 9 1-(R^2) = 0 adj. R^2= 1 Section A: 1st Order, 2nd Order and 3rd Order Models. 1. Already completed...see previous page. Section B: The Most Appropriate Model 1. [3] Of the three Profit models1st, 2nd or 3rd orderidentify the most appropriate for estimating purposes, according to the \"highest percent variation explained\" criteriona criterion based on [(R2)] or [(R2)adj]. Section C: Calculations using The Most Appropriate Model Answer the following questions using the most appropriate model from Section B above. Assume that, unless otherwise indicated, the restricted domain for \"x\" is 0 x 840. 1. [6] Estimate Profit \"P\" @ x = 0, x = 240 and x = 310 units. 2 2. [2] Estimate how many units \"x\" of the product must be sold in order to generate a Profit of $0.00. 3. [4] Estimate how many product units \"x\" should be sold per sales period to optimize this product's Profit \"P\" and the value of \"P\" at this \"x\" value. Assume market constraints suggest the maximum number of units that actually can be sold per sales period may not exceed... (a). ...840 (0 x 840 units). (b). ...500 (0 x 500 units). 4. [4] Use differential calculus to develop a mathematical expression for estimating marginal Profit \"mP\" for this product. Estimate \"mP\" using the expression if initially... (a). ...760 units were sold. (b). ...400 units were sold. 5. [2] Identify the value of \"x\" at any inflection point...then...use this \"x\" value to calculate the associated value of \"P\". 6. [2] Estimate the smallest number of units \"x\" that must be produced and sold in order to generate a Profit of $916,815. PART II: 1st/2nd/3rd Order Models As manager of a particular product line in Mumbai, you have data available for the past 15 sales periods. This data associates your product line's units sold \"q\" and total expenditures \"e\" (in millions of Rupees) on advertising during a previous sales period. Product N AdExp [e] (x10^6) UnitsSold [q] 3 10 20 40 60 80 100 120 140 160 180 200 220 240 250 260 54270 65010 83130 97570 109290 119250 128410 137730 148170 160690 176250 195810 220330 234750 250770 Section A: 1st Order Model, 2nd Order Model or 3rd Order Model? 1. Use Excel's Chart feature to graph a plot of the data, assuming q = (e). a. [4] Add the most appropriate 1st order \"trend line\