Concept explainers
EXERCISES
Reminder Round all answers to two decimal places unless otherwise indicated.
Fixed and Variable Costs The fixed cost for a manufacturing company are the costs, such as rent or repayment of a startup loan, that the company must pay each month no matter how many items are produced. The variable cast is the cost of producing a single item. Assume that when a company produces
Identify the fixed costs and the variable cost in this equation.
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Chapter 5 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Flood Control A river is 8 feet above its flood stage. The water is receding at a rate of 3 inches per hour. Write a mathematical model that shows the number of feet above flood stage after t hours. Assuming the water continually recedes at this rate, when will the river be 1 foot above its flood stage?arrow_forwardGrade Point Average In many universities students are given grade points for each credit unit according to the following scale: A 4 points B 3 points C 2 points D 1 point F 0 point For example, a grade of A in a 3-unit course earns 43=12 grade points and a grade of B in a 5-unit course earns 35=15 grade points. A students grade point average GPA for these two courses is the total number of grade points earned divided by the number of units; in this case the GPA is (12+15)8=3.375. a Find a formula for the GPA of a student who earns a grade of A in a units of course work, B in b units, C in c units, D in d units and F in f units. b Find the GPA of a student who has earned a grade of A in two 3-unit courses, B in one 4-unit courses and C in three 3-unit courses.arrow_forwardCan you help with parts d, e, and f please? The Admission director for a college far from mart and town believes that an inverse relationship exists between a private college's average discount rate(determined by the average amount of scholarships students receive) and the annual yield (the percentage of admitted students who actually attend). The Director's independent variable is a private college's discount rate measured as a percentage, and the dependent variable is the college's annual yield measured as a percentage. The following results were obtained for a sample of 30 private colleges: x- Discount rate(percentage) - range: 35 to 72 percent y- Annual Yield(percentage) - range: 12 o 81 percent Σxi = 1612 Σyi = 898Σxiyi = 44,377Σxi2 = 89,790Σyi2 = 35,704a. Calculate the sample regression line's slope estimate. Interpret the sample regression line's slope estimate.b. Calculate the sample regression line's intercept estimate. Interpret the sample regression line's intercept…arrow_forward
- A hamburger factory produces 40,000 hamburgers each week. The equipment used costs $8,000 and will remain productive for three years. The labor cost per year is $12,000. What is the productivity measure of "units of output per dollar of input" averaged over the three-year period? Assume that there are 52 weeks per year. Round your answer to one decimal place. Productivity: hamburgers/dollar We have the option of $10,000 equipment, with an operating life of four years. It would reduce labor costs to $9,500 per year. Should we consider purchasing this equipment (using productivity arguments alone)? Assume that there are 52 weeks per year. Round your answer for productivity to one decimal place. For the expensive machine, productivity is hamburgers/dollar input. Because the productivity of the expensive machine is , it would be a investment based on this single criterion.arrow_forwardScreenshot attached. Find the instantaneous rate of change of demand with respect to price when the price is $6.75. Round to the nearest hundredth (2 decimal places) pounds per dollararrow_forwardYanter Outfitten manutactures and vets etreme-cold sleeping bag The table below shown the price-denand and total cost data where Revenue Model pewholesale price in dollansi of a sleeping bag for aweekly demand of eseeping bag Csthe total cost n doan of producingsleeping ba Using the regression model computed above, find a model for the weekly revenue, using as the independent variable. leeping bagl 340 13.000 NOTE: Do not calculate another regression. Use the price equation to find a model for revenue R()-p- 120 225 h4.300 Find a quadratic regression equation for the price-demand data, using as the independent variable. 180 155 18.500 Pa+ be ++c? R(2) - p-z- (a + bz + cz) ar + ba? + c 220 30 1.000 Round a to the nearest integer, round b to 2 decimal places, and round e to 4 decimal places. Cost Model Find a linear regression model for the weekly cost data, using a as the independent variable. C(x) = ma +k %3D Round m to 1 decimal place, and round k to the nearest integer. What is m?…arrow_forward
- Can you help with parts a, b and c please? The Admission director for a college far from mart and town believes that an inverse relationship exists between a private college's average discount rate(determined by the average amount of scholarships students receive) and the annual yield (the percentage of admitted students who actually attend). The Director's independent variable is a private college's discount rate measured as a percentage, and the dependent variable is the college's annual yield measured as a percentage. The following results were obtained for a sample of 30 private colleges: x- Discount rate(percentage) - range: 35 to 72 percent y- Annual Yield(percentage) - range: 12 o 81 percentΣxi = 1612 Σyi = 898Σxiyi = 44,377Σxi2 = 89,790Σyi2 = 35,704 a. Calculate the sample regression line's slope estimate. Interpret the sample regression line's slope estimate.b. Calculate the sample regression line's intercept estimate. Interpret the sample regression line's intercept estimate.…arrow_forwardWhat is the right answer ?arrow_forwardThe demand equation for the BWS Bluetooth wirelearrow_forward
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