Question

Objective: Apply elementary mathematical concepts and quantitative methods in business decision making under certainty.

Create a context: Introduce a real-world business situation or an imagined business scenario that may benefit from the "math" presented in the prior two weeks (Weeks 1 and 2 - see the objective stated in bold above). While creating the context, ask yourself: What business use cases may benefit from the quantitative methods offered last week and this week? Basi algebraic numbers, binary operations, integral exponents, equations, functions, or derivates. Pick one. You can use Google or other search tools, or your own workplace experience, to create the context.

Show with examples how the "math" or quantitative methodology introduced in the prior two weeks relate to the business use case you introduced. (e.g., does the math/methodology help to resolve a business problem?) Be specific in your description of how you can use the quantitative information in connection with the business case (your context) you described. Give examples. Use technical terminology when necessary.

Reflect on your learning by answering these questions: What changes have you observed in your own learning or knowledge of math/quantitative methods as a result of the topics introduced in Weeks 1 and 2 of this course? What did you find most valuable or useful for your MBA education and/or your current/future career? (As you articulate your thoughts for Part 3, be original: Do not repeat the business context or situation you described in Parts 1 and 2.

Answer 1

A canning factory produces two types of cans of soda, A and B, which are sold for $1 per unit of an A, and $1.20 per unit of can B. However, the production of cans of soda is limited to 1000 cans per day, and the amount of soda is limited to 360 L. The volume of a can of soda A is 300 cc and the volume of a can of soda B is 400 cc. How many cans of soda of both types must be produced to maximize the revenues ?

Let R be the total revenue from the production. As one can of soda A costs $1 and one can of soda B costs $1.20, the total revenue is given by this formula:

Where x is the amount of cans of soda A, and y is the amount of cans of soda B.

According to the problem, the total amount of cans of soda is limited to 1000 per day, so the sum of x and y cans can not be hhigher than 1000. So, we get...

Also, according to the problem, the total amount of canned soda must not surpass 360 L (360.000 cc). So, we get...

And, of course, the amount of cans must be a whole number.

So, the objective is to maximize the function R = x + 1.2y, subject to the restrictions above. A problem like this can be solved by Linear Programming, using the graphical method, or the Simplex Method.