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Question about sets and set theory:
Why is it important to be able to identify sets and theory as related to business?

What applications do you think functions have for the business world?
Can functions be used to predict next year's profits, or how much your company will grow?

Why is it important to understand linear equations in business?
Can you provide examples where the relationship between items that can be affect by management and items that management wished to achieve or attain may be 'linear'?
Can you think of items for which the relationship is not linear?

What do you think is the typical situation in the business world: risk or uncertainty?
Can you think of situations in the business world or other real life situations where you would need to estimate probabilities?

From a business prospective, which measurements is more important, the mode, the mean, or the median?
Provide examples (Business related) that demonstrate the appropriateness of one of these measures and the inappropriateness of the other two in a particular situation?
Can you think of a situation where another one of the measures is more appropriate of relevant?

What are two concepts that you believe are more applicable in business administration.

#### Solution Preview

Please refer to the attached file for the response.

OVERVIEW OF SELECTED CONCEPTS

Sets and set theory
Importance
To solve a business problem, decisions are to be made. Failure or success in solving the problem would be very much dependent on how well the real issue was identified, on the logic used in determining the variables or factors related to the issue, on the analysis utilized for each variable and their interrelationships, on the evaluation of alternatives, and on the final decision arrived at.
According to the so-called decision theory, there are six steps involved (Render et al., 2003) in decision making, namely: 1) clearly define the problem at hand, 2) list the possible alternatives, 3) identify the possible outcomes or states of nature, 4) list the payoff or profit of each combination of alternatives and outcomes, 5) select one of the mathematical decision theory models, and 6) apply the model and make your decision.
The above discussion indicates that the use of a mathematical theory would be of help in evaluating the set of alternatives and possible outcomes that would serve as basis in making a decision that would solve an identified problem.

Functions
Applications of functions for the business world
Functions show determinants of a particular variable. As such, a denotation of
D = f (price, income, taste and preference, promotions)
would indicate that demand for a good is a function of its price, the income of the consumer, his taste and preference, and the promotional strategies of the seller or the producer of the good.
Functional relationship would help a decision maker. In the example stated earlier, a producer or a marketer can influence demand by coming up with a reasonable price, or a price that would be appropriate to income and purchasing power of the target buyers, a product that would meet the taste and preference of the buyer, and an effective promotional strategy.
Another online source noted that function is a relation in which each element of the input is associated ...

#### Solution Summary

The expert examines quantitative methods in business. Why it is important to understand linear equations in business are given.

\$2.19

Case Problem 2: Production Strategy

1. Let BP100 = the number of BodyPlus 100 machines produced
BP200 = the number of BodyPlus 200 machines produced

Max 371BP100 + 461BP200
s.t.
8BP100 + 12BP200 <= 600 Machining and Welding
5BP100 + 10BP200 <= 450 Painting and Finishing
2BP100 + 2BP200 <= 140 Assembly, Test, and Packaging
-0.25BP100 + 0.75BP200 >= 0 BodyPlus 200 Requirement

BP100, BP200 greater than of equal to 0

See attachment for graph

Optimal solution: BP100 = 50, BP200 = 50/3, profit = \$26,233.33. Note: If the optimal solution is rounded to BP100 = 50, BP200 = 16.67, the value of the optimal solution will differ from the value shown. The value we show for the optimal solution is the same as the value that will be obtained if the problem is solved using a linear programming software package such as Excel Solver.

2. In the short run the requirement reduces profits. For instance, if the requirement were reduced to at least 24% of total production, the new optimal solution is BP100 = 1425/28, BP200 = 225/14, with a total profit of \$26,290.18; thus, total profits would increase by \$56.85. Note: If the optimal solution is rounded to BP100 = 50.89, BP200 = 16.07, the value of the optimal solution will differ from the value shown. The value we show for the optimal solution is the same as the value that will be obtained if the problem is solved using a linear programming software package such as Excel Solver.

3. If management really believes that the BodyPlus 200 can help position BFI as one of the leader's in high-end exercise equipment, the constraint requiring that the number of units of the BodyPlus 200 produced be at least 25% of total production should not be changed. Since the optimal solution uses all of the available machining and welding time, management should try to obtain additional hours of this resource.

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