After substituting above values in equation 1 we get Qd 502458 11741 10914

After substituting above values in equation 1 we get

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After substituting above values in equation (1), we get, Qd = 5024.58 + 117.41 * 109.14 136.62 * P 0.2823 * 7620.601 + 7.87 * 1247.31 Qd = 25,503.74 136.62P At this point of time, let’s remember this, Total Revenue (TR) = P * Qd ……. (2) Let’s substitute equation 1 in equation 2, we will get, TR = P * (25,503.74 136.62P) = 25,503.74P 136.62P^2 …… (3) Time for some Differentiation, performing differentiation on both sides w.r.t P d(TR)/d(P) = 25,503.74 * d(P)/d(P) 2 * P * 136.62 * d(P)/d(P) d(TR)/d(P) = 25,503.74 273.24P 0 = 25,503.74 273.24P (because, at TR max, slope is zero) Therefore, P = 93.34
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Now, substituting P = 93.34 in 3, we will get: TR = 25,503.74 * 93.34 136.62 * 93.34 * 93.34 TR = 1190237.07 Finally, in scenario 1, max TR = 1190237.07 at optimum price, P = 93.34 In scenario 2, the values to consider for predicting the optimum price where total revenue can be maximized are: - Competitive Price = 115.69 (This value is obtained after we increased 109.14 by 6% as said in question) Income per capita = 7620.601 (This value is obtained after we increased 7545.15 by 1% as said in question) Promotional Expenditure = 1247.31 Now, again taking our demand equation from above, Qd = 5024.58 + 117.41 (Price of competitor's products) - 136.62 (Price of Maa Mustard Oil) - 0.2823 (Per capita income of consumers) + 7.87 (Promotional expenditure of Maa mustard oil) ……. (1) After substituting above values in equation (1), we get, Qd = 5024.58 + 117.41 * 115.69 136.62 * P 0.2823 * 7620.601 + 7.87 * 1247.31 Qd = 26,272.77 136.62P Let’s recall equation 2 from scenario 1, TR = P * Qd TR = P * (26,272.77 136.62P) = 26,272.77 * P 136.62 * P^2 Performing differentiation on both sides with P, we will get, d(TR)/d(P) = 26,272.77 * d(P)/d(P) 2 * P * 136.62 * d(P)/d(P) d(TR)/d(P) = 26,272.77 - 273.24P 0 = 26,272.77 273.24P (because, at TR max, slope is zero) P = 96.15 Now, substituting P = 96.15 in TR equation, we will get:
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