Quantitative Analysis and Decision Making
Problem 3
Qualitative approaches entail making decisions based on previous experiences with regards to a similar situation (Östlund et al., 2011). In essence, one is likely to analyze the situation at hand and experience a familiar feel, commonly referred to as an intuition, and then handle the decision in a similar manner as how it was handled in the past. Such an approach is okay in situation which do not require a lot of thought as the intuition may result in a positive outcome. When there was no any similar experience of the problem at hand then the need for a quantitative approach comes into play. A quantitative approach entails one taking his or her time in gathering data and information needed in order to make a decision (Brannen, 2017). A quantitative approach is used when more details that is required is complex in nature.
A good understanding of both quantitative and qualitative approaches in making decision is vital for a decision maker or a manager since it is more beneficial if they can combine the two approaches in any situation (Brannen, 2017). Combining the two approaches to a problem or an issue means that the decision maker or manager will get a better outcome to the problem and therefore will not recur.
Problem 5
The benefits of analyzing and experimenting with a model compared to a real situation or objects is that the user can make interpretations regarding a real situation through the review and examination of the model. On the other hand, utilization of a model is less expensive and requires less time compared to an actual object or a real situation. Moreover, models have the benefit of reducing the risk which is associated with the experimentation with real situations.
Problem 7
There are many factors to consider when planning a trip during the weekend to the city. These factors need to be put into consideration. A model needs to be developed to determine the round-trip gasoline cost. The uncontrollable inputs for such a trip that is known and cannot be varied is the need to drive d miles away. The number of miles is affected by the objective function and the constraints. The other known variable is weather and there is a chance that the weather may change. Other assumptions that can be made is the weight in the car which will stay relatively constant as more weight would result in more fuel consumption. The uncontrollable costs listed above are necessary in treating this model as a deterministic model. These factors are acceptable to me since they are known and cannot be changed.
Problem 10
Total Units = x + y
Total cost = 0.20x + 0.25y
5000 = x + y
y ≤ 3000 Minneapolis
x ≤ 4000 Kansas City
Min 0.20x + 0.25y
s.t.
x + y = 5000
y ≤ 3000
x ≤ 4000
x, y ≥ 0
Problem 11
d = 800 – 10*20
d = 600 Units
d = 800 – 10*70
d = 100 Units
d = 800 – 10*26
d = 540 Units
d = 800 – 10*27
d = 530 Units
Demand by decrease by 10 units when there is an increases in per-unit price from $26 to $27
d = 800 – 10*42
d = 380 Units
d = 800 – 10*43
d = 370 Units
Demand decreases by 10 units when per unit price increases from $42 to $43
d = 800 – 10*68
d = 120 Units
d = 800 – 10*69
d = 110 Units
Demand decreases by 10 units when per unit price increases from $68 to $69
Thus, there is a negative relationship between per-unit price and the annual demand for the products in units. Therefore, a one unit increase in the per-unit price leads to a 10 unit decrease in demand.
Total Revenue = Annual Demand * Unit Price
TR = (800 – 10P)*P
TR = 800P – 10P2
TR when p=30
800*30 – 10*30*30 = 15,000
TR when p = 40
800*40 – 10*40*40 = 16,000
TR when p = 50
800*50 – 10*50*50 = 15,000
Thus, total revenue is maximized when price is equal to $40.
e.
The expected annual demand is:
d = 800 – 10*40
d = 400 units
The expected total revenue is:
TR = 800*40 – 10*40*40
TR = $16,000
Problem 13
a.
TC = 9600 + 60x
Where TC is total cost and x is the number of students
b.
y = TR – TC
y = 600x – (9600 + 60x)
y = 600x – 9600 – 60x
Where y is the profit, TR is the total revenue, TC is the total cost and x the number of students
y = 600*30 – 9600 – 60*30
y = $6,600
d.
y = 600x – (9600 + 60x)
0 = 600x – (9600 + 60x)
9600 + 60x = 600x
9600 = 600x – 60x
9600 = 540x
9600/540 = 540x/540
x = 17.78
Thus, the breakeven point is 18 students
Problem 16
Objective Function:
Max Z = 6x + 4y
Constraints
50x+30y ≤ 800,000
50x ≤ 500,000
30y ≤ 450,000
Problem 17
sj = sj−1 + xj − dj
xj ≤ Cj
sj ≥ Ij
References:
Brannen, J. (2017). Combining qualitative and quantitative approaches: an overview. In Mixing methods: Qualitative and quantitative research (pp. 3-37). Routledge.
Östlund, U., Kidd, L., Wengström, Y., & Rowa-Dewar, N. (2011). Combining qualitative and quantitative research within mixed method research designs: a methodological review. International journal of nursing studies, 48(3), 369-383.
