Math 1325

Applications of Extrema

Name: ­_________________________________________ Date: ________________________

Please review the instructions on the last page before beginning this assignment.

The marketing research department for a computer company used a large city to test market their new computer. They found that the relationship between the price
p
(dollars per unit) and the demand
x
(units per week) for the new computer was given approximately by the equation .

1. Explain, in writing, how to find a formula for the total revenue function if given the unit price
p
and number of units sold
x. Find the formula for the total revenue from the sale of
x
units of the new computer.

2. Explain, in writing, how you would determine the maximum revenue if given a total revenue function. Find the number of computers that must be sold in order to maximize the revenue formula in #1.

3. Find the maximum revenue for the number of computers found in #2. Briefly explain your result.

Math 1325 Applications of Extrema Name: _________________________________________ Date: ________________________ Please review the instructions on the last page before beginning this assignment. The marketing research department for a computer company used a large city to test market their new computer. They found that the relationship between the price p (dollars per unit) and the demand x (units per week) for the new computer was given approximately by the equation . 1. Explain, in writing, how to find a formula for the total revenue function if given the unit price p and number of units sold x. Find the formula for the total revenue from the sale of x units of the new computer. 2. Explain, in writing, how you would determine the maximum revenue if given a total revenue function. Find the number of computers that must be sold in order to maximize the revenue formula in #1. 3. Find the maximum revenue for the number of computers found in #2. Briefly explain your result. Your grade on this assignment has three components: 1) the accuracy of your response with regard to the questions about the math content, 2) your ability to identify and analyze the problem, and 3) your explanation of the solution Regarding your writing, be sure that you: · fully identify and explain the formula needed for the problem and support them with evidence from your textbook; · select the proper method for solving the problem and explain your selection; · explain, in writing, the method for utilizing the formula; · draw the appropriate conclusion and provide a coherent argument for the solution; · express your ideas creatively; · use language that is clear and that accurately expresses your ideas, think about the vocabulary you use; and · use a variety of sentence structures and be sure your spelling, grammar and punctuation are correct The following rubric will be used to evaluate your critical thinking skills on this assignment. Criteria Highly Competent (4) Mostly Competent (3) Needs Improvement (2) Not Competent (1) 1. Identification of Problem or Issue Problem or issue clearly identified, explicit Problem or issue identified implicitly or incompletely described Problem or issue present, but a little ambiguous Problem or issue ambiguous or not present 2. Analysis of Problem, Issue, or Investigation 2.1 Method(s) Method(s) selected and used appropriately Some inappropriate choice or use of method(s) Choice or use of method(s) needs improvement Completely inappropriate choice and use of method(s) 2. Analysis of Problem, Issue, or Investigation: 2.2 Alternative Points of View Thoroughly considered multiple alternate points of view Thoroughly considered attention to one alternate view Some attention to at least one alternate view Obvious alternate views ignored 3. Credibility of Resources or Source Materials Appropriate, relevant and credible resources and source materials Most resources and source materials relevant, appropriate and credible Some resources and source materials relevant, appropriate and credible No resources or source materials relevant, appropriate or credible 4. Conclusion or Problem Solution: 4.1 Integration Ideas well integrated into a coherent argument, solution, presentation Ideas integrated into a somewhat coherent argument, solution, presentation Some connections to a few ideas are made Ideas lack connection or coherence 4. Conclusion or Problem Solution: 4.2 Conclusions, Solution(s) Conclusions, solutions based on evidence or sound methods Most conclusions, solutions based on evidence Some unwarranted conclusions drawn, or some solution errors Conclusions, solutions unwarranted; maintains preconceived views regardless of evidence or need for different solution 5. Creativity, Innovation Fresh ideas, reflecting in- depth student engagement with the topic Some new insights, reflects some in depth consideration of topic Very few new insights; primarily based on collection and repetition of other people’s ideas, products, images No evidence of engagement, new ideas on topic; work simply a rehash of other people’s ideas 2 08 . 0 3750 ) ( x x p - =