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

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: