When mathematicians are presented with a linear programming problem, they will not only determine the optimal solution but will also supply what are called shadow prices for each resource. This chapter project develops the concept of a shadow price.
Consider the furniture manufacturing problem. The constraint for finishing is
Determine the optimal solution for the revised linear programming problem. What is the new maximum profit? By how much was the profit increased due to the additional hour for finishing? This amount is the shadow price.
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Finite Mathematics & Its Applications (12th Edition)
- At the Pizza Dude restaurant, a 12-in. pizza costs 5.40 to make, and the manager wants to make at least 4.80 from the sale of each pizza. If the pizza will be sold by the slice and each pizza is cut into 6 pieces, what is the minimum charge per slice?arrow_forwardIf during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.arrow_forwardIn Example 3, if the accountant earns a profit of 100 on each individual return and a profit of 175 on each business return, find the maximum profit. An accountant prepares tax returns for individuals and for small businesses. On average, each individual return requires 3 hours of her time and 1 hour of computer time. Each business return requires 4 hours of her time and 2 hours of computer time. Because of other business considerations, her time is limited to 240 hours, and the computer time is limited to 100 hours. If she earns a profit of 80 on each individual return and a profit of 150 on each business return, how many returns of each type should she prepare to maximize her profit?arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,