A recent budget for the California State University system projected a fixed cost of $486,000 at each of five off-campus centers, plus a marginal cost of $1140 per student.  (a) Find a formula for the cost at each center, C(x), as a linear function of x, the number of students. (b) The budget projected 500 students at each center. Calculate the total cost at each center.(c) Suppose, due to budget cuts, that each center is limited to $1 million. What is the maximum number of students that each center can then support?

Using Social Security Administration data for selected years from 2012 and projected to 2050, the U.S. consumer price index (CPI) can be modeled by the function y = 0.0682x² + 1.76x + 96.0 where x is the number of years past 2010 and y is the CPI in dollars. With a reference of 100 in 2012, a CPI of 120 in another year means that goods and services costing $100 in 2012 are expected to cost $120 in that other year (a) Use a table to determine a viewing window that shows a complete graph of this function for the years from 2010 to 2050. 2050 corresponds to an x value of which corresponds to a y value of The y maximum should be -Select-than this function value (b) Graph the function. y 300 250 200 150 100 50 0 y 300 250 200 150 100 50 X = Need Help? 51 F Partly sunny 10 10 20 Read It 20 30 30 T X 40 40 y 300 250 200 150 100 50 0 0 10 (c) Use the graph to estimate when the CPI is predicted to reach 250. (Round your answer to the nearest whole year.) years 20 30 Q Search 40 y 300 250 200…

If x represents the number of items produced, (a) write a cost function, (b) find a revenue function if each item sells for the price given, (c) state the profit function, (d) determine analytically how many items must be produced before a profit is realized (assume whole numbers of items), and (e) support the results of part (d) graphically. The fixed cost is $600, the cost to produce an item is $25, and the selling price of the item is $50. (a) The cost function is C(x) = (Simplify your answer. Do not factor.) (b) The revenue function is R(x)= (Simplify your answer. Do not factor.) (c) The profit function is P(x) = (Simplify your answer. Do not factor.) ← (d) At least items must be produced before a profit is shown. (Type a whole number.) (e) Choose the correct graph to the right. O A. 2100 O C. Dollars Items produced 2100 Items produced Q O B. 2100 O D. Dollars 2100 Items produced Items produced Q ✔