Use the method of Lagrange multipliers to solve this exercise. Hercules Films is deciding on the price of the video release of its film Son of Frankenstein. Its marketing people estimate that at a price of p dollars, it can sell a total of q = 240,000 – 12,000p copies. What price will bring in the greatest revenue? p = $

Use the method of Lagrange multipliers to solve this exercise. Hercules Films is deciding on the price of the video release of its film Son of Frankenstein. Its marketing people estimate that at a price of p dollars, it can sell a total of q = 240,000 – 12,000p copies. What price will bring in the greatest revenue? p = $

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter4: Systems Of Linear Equations

Section4.3: Solve Mixture Applications With Systems Of Equations

Problem 158E: The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The...

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The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The manufacturer also has fixed costs each month of $8,000. (a) Find the cost function C when x energy drinks aremanufactured. (b) Find the revenue function R when x drinks are sold. (c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid. (d) Find the break-even point. Interpret what the breakeven point means.
The manufacturer of a weight training bench spends $15 to build each bench and sells them for $32. The manufacturer also has fixed costs each month of $25,500. (a) Find the cost function C when x benches are manufactured. (b) Find the revenue function R when x benches are sold. (c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid. (d) Find the break-even point. Interpret what the break-even point means.
The manufacturer of a water bottle spends $5 to build each bottle and sells them for $10. The manufacturer also has fixed costs each month of $6500. (a) Find the cost function C when x bottles are manufactured. (b) Find the revenue function R when x bottles are sold. (c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid. (d) Find the break-even point. Interpret what the break-even point means.
Use your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.