Patricia's rating for each of the three criteria, taste, location, and pricing, for two restaurants is stated in the table below on a scale of 1 to 100:
Steakhouse Pizzahouse TasteLocationPrice 805565 708050
The taste of foods is the most essential selection criteria in the Los Angeles suburbs, while location is the least important, with price falling somewhere in the middle. To represent the relative utility of the two restaurants in the Los Angeles suburbs, consider the weight of taste to be 3. Since the taste attribute is two times as important as the price and three times as important as the price and three times as important as the location, the relative weight for these two attributes will be 2 and 1 respectively. Now, let us compute the value of expected utility for these two restaurants:
Steak Restaurant’s expected utility in suburban area of Los Angeles =
(3 × 80 + 1 × 55 + 2 × 65) ÷ (3+1+2) = (240 + 55 + 130) ÷ 6= 425 ÷ 6 = 70.83
Similarly, Pizza Restaurant’s expected utility in suburban area of Los Angeles =
(3 × 70 + 1 × 80 + 2 × 50) ÷ (3+1+2) = (210 + 80 + 100) ÷ 6= 390 ÷ 6 = 65
As evident from the expected utility calculation result, Patricia need to open a steak restaurant at the location of suburban area, Los Angeles, if she wants to earn greater profitability.
Proceeding in a similar way, the expected utility at Los Angeles Metropolitan Area can be computed as follows: (here, weight of the location, price and taste are 3, 2 and 1 respectively).
Steak Restaurant’s expected utility in the Metropolitan area of Los Angeles =
(1 × 80 + 3 × 55 + 2 × 65) ÷ (1+3+2) = (80 + 165 + 130) ÷ 6= 375 ÷ 6 = 62.50
Similarly, Pizza Restaurant’s expected utility in the Metropolitan area of Los Angeles =
(1 × 70 + 3 × 80 + 2 × 50) ÷ (1+3+2) = (70 + 240 + 100) ÷ 6= 410 ÷ 6 = 68.34
Since the expected utility of pizza restaurant is higher, Patricia should start pizza restaurant business at the metropolitan area of Los Angeles.
In case, Patricia falls in a situation, where the probability of finding a venue for the restaurant in the suburban area is 0.7 against 0.3 in the metropolitan area, she should go for steak restaurant at the suburban area because the yield of the expected utility is higher at this place: 0.7 × 70.83 = 49.581 against 0.3 × 68.34 = 20.502.
In real world setting of the business, this sort of decision–making problem arises when a company wants to segment its market for two of its products or when a company wants to make a decision on acquiring one of two different types of business.
Benefits:
Provides a means of transforming qualitative attributes to quantitative values to facilitate numerical computation and easy comparison,
Facilitate easy decision-making solutions without requiring extensive research or manipulation.
Drawbacks:
Value assignment problem to attributes is not consistent across different situations, locations, scenario. It suffers from observer’s bias.
External variables that may influence the decision are not accounted for in this type of decision-making process, which may lead to a wrong selection.
Solution to Problem #2:
The percentage by which the demand changes due to the unit change in the price defines the price elasticity of demand of Newton’s donuts. Mathematically, it can be expressed as:
Price elasticity of demand =
Here, Qx = –14 – 54Px + 45 Py + 0.62 Ax
Differentiating with respect to Px, we get:
= – 0 –54 × 1 + 45 × 0 + 0.62 × 0 = –54; This gives us the price elasticity of demand
of Newton’s donuts. The negative sign indicates the change in demands in response to the
price is opposite i.e. for every unit increase in the bagel price, the demand decreases by
54 units.
The demand function of Newton’s donuts is:
Qx = –14 – 54Px + 45 Py + 0.62 Ax
It can be rearranged to:
54Px = –14 – Qx + 45 Py + 0.62 Ax
Px =
The above equation indicates that the variable Px depends on the independent variables Qx, Py and Ax. We can infer that the price of the Newton’s donuts depends on the demands of the donuts, competitors’ donuts price and the amount of money spent in advertising.
Assuming, the price of the competitors and the advertising cost as constants, we can write, Px = = ; this is the required inverse demand curve.
The demand function of Newton’s donuts is:
Qx = –14 – 54Px + 45 Py + 0.62 Ax
At the present price, Px = $0.95, it becomes,
Qx = –14 – 54 × 0.95 + 45 × 0.64 + 0.62 × 120 = 37.9 Thousand
Profit = Revenue – Production cost = Px × Qx – Unit Cost of production× Qx
= 37,900 × 0.95 – 37,900 × 0.15 [unit cost of production = $0.15]
= $30,320
In general, Profit = Revenue – Production cost
= Px × Qx – Unit Cost of production× Qx
= ( × Qx – 0.15× Qx
The profit maximization function,
= ( – 0.15
Equating it to zero,
= ( – 0.15 = 0
( – 0.15 = 0
2Qx = 89.2 – 0.15 × 54 = 81.1
Qx = 40.55 thousands = 40,550 bagels
Price, Px = = $0.90
The maximum profit = 40,550 × 0.90 – 40,550 × 0.15 = $30,412.50;
The difference from the previous profit = $30,412.50 – $30320 = $92.5;
So, we can conclude that if the bagel price can be reduced by $0.05, overall profit
will increase by $92.5.
The demand function of Newton’s donuts is:
Qx = –14 – 54Px + 45 Py + 0.62 Ax
Let’s find the differentiation of the demand with respect to the advertising expenses:
= –0 – 54 × 0 + 45 × 0 + 0.62 = 0.62 = 62%; evidently, for each unit increase in advertising expense, corresponding increase in demand is 62%. So the advertising expense should be increased.
