Mastering Growth Tasks in Math 135: Key Problem Solving
School
California State University, Fullerton**We aren't endorsed by this school
Course
MATH 135
Subject
Mathematics
Date
Dec 12, 2024
Pages
2
Uploaded by BaronFire17590
CSU FULLERTON COLLEGE OF NATURAL SCIENCES & MATHEMATICS, DEPARTMENT OF MATHEMATICS MATH 135 LECTURE NOTES – VERSION 1 CHAPTER 6 – GUTASKUS 1 Chapter 6 Growth Task Instructions: Complete the following problems to the best of your ability at the beginning of the chapter. In the initial stage of the Growth Task, we are aiming to measure where your learning in this chapter begins. Write down any information you know about the problem, solve the problem, or write “I don’t know.” That is okay! Just give each problem your best attempt. You may use your textbook and calculator, but no other resources, or solving applications like photomath, mathway, chegg, etc. 1.Determine 𝑓𝑓𝑥𝑥and 𝑓𝑓𝑦𝑦when 𝑧𝑧= 3�𝑥𝑥𝑥𝑥3−5𝑥𝑥𝑒𝑒𝑦𝑦+𝑥𝑥5𝑦𝑦32.Determine 𝑓𝑓𝑥𝑥𝑥𝑥,𝑓𝑓𝑥𝑥𝑦𝑦,𝑓𝑓𝑦𝑦𝑥𝑥,and 𝑓𝑓𝑦𝑦𝑦𝑦when 𝑓𝑓(𝑥𝑥,𝑥𝑥) = (𝑥𝑥2− 𝑥𝑥2)3
CSU FULLERTON COLLEGE OF NATURAL SCIENCES & MATHEMATICS, DEPARTMENT OF MATHEMATICS MATH 135 LECTURE NOTES – VERSION 1 CHAPTER 6 – GUTASKUS 2 3.A company sells two sizes of microwave ovens: the small size and the large size. The demand functions for the microwave ovens are given by 𝑝𝑝𝑠𝑠𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚= 150−0.5𝑥𝑥 −0.2𝑥𝑥𝑝𝑝𝑚𝑚𝑚𝑚𝑎𝑎𝑎𝑎𝑎𝑎= 250−0.1𝑥𝑥 −0.5𝑥𝑥Where 𝑝𝑝𝑠𝑠𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚and 𝑝𝑝𝑚𝑚𝑚𝑚𝑎𝑎𝑎𝑎𝑎𝑎are the prices of the two sizes in dollars, 𝑥𝑥is the units of the small mixrowave, and 𝑥𝑥is the units of the large microwave ovens sold each week. a.Determine the total revenue function 𝑅𝑅(𝑥𝑥,𝑥𝑥)b.Determine 𝑅𝑅𝑥𝑥(50,30)and interpret. c.Determine 𝑅𝑅𝑦𝑦(50,30)and interpret. 4.A company operates two plants, Plant A and Plant B, which produce the same product. The total annual cost function, in thousands of dollars, for each plant is 𝐶𝐶𝐴𝐴(𝑥𝑥) = 9 + 0.04𝑥𝑥2and 𝐶𝐶𝐵𝐵(𝑥𝑥) = 6 +0.04𝑥𝑥2, where x and y are hundreds of items produced in each plant. The total annual demand for𝑞𝑞=𝑥𝑥+ 𝑥𝑥can expressed by 𝑝𝑝= 𝐷𝐷(𝑞𝑞) = 65−0.04𝑞𝑞.a.Determine the total annual profit function 𝑃𝑃(𝑥𝑥,𝑥𝑥).b.Determine how many units of the product each plant should produce and sell in order to maximize the company's total annual profit.