Suggested languages for you:

Americas

Europe

Problem 396

Find a basic feasible solution to the problem: Maximize $\quad \mathrm{x}_{1}+2 \mathrm{x}_{2}+3 \mathrm{x}_{3}+4 \mathrm{x}_{4}$ while satisfying the conditions $$ \begin{aligned} &\mathrm{x}_{1}+2 \mathrm{x}_{2}+\mathrm{x}_{3}+\mathrm{x}_{4}=3 \\ &\mathrm{x}_{1}-\mathrm{x}_{2}+2 \mathrm{x}_{3}+\mathrm{x}_{4}=4 \\ &\mathrm{x}_{1}+\mathrm{x}_{2}-\mathrm{x}_{3}-\mathrm{x}_{4}=-1 \end{aligned} $$ \(\mathrm{x}_{1}, \mathrm{x}_{2}, \mathrm{x}_{3}, \mathrm{x}_{4} \geq 0\)

Expert verified

A basic feasible solution for this problem cannot be found using only the current tableau. Further analysis, such as using the dual simplex method, is necessary to find a feasible solution given the constraints. The current tableau gives the solution \(x_{1} = 0, x_{2} = 0, x_{3} = 0, x_{4} = 0, x_{5} = 3, x_{6} = 4, x_{7} = -1\), but this is not feasible as \(x_{7} < 0\).

What do you think about this solution?

We value your feedback to improve our textbook solutions.

- Access over 3 million high quality textbook solutions
- Access our popular flashcard, quiz, mock-exam and notes features
- Access our smart AI features to upgrade your learning

Chapter 17

Show through the simplex method and then graphically that the following linear program has no solution. Maximize \(\quad 2 \mathrm{x}+\mathrm{y}\) subject to $$ \begin{aligned} &-x+y \leq 1 \\ &x-2 y \leq 2 \end{aligned} $$ \(\mathrm{x}, \mathrm{y} \geq 0 .\)

Chapter 17

According to the Fundamental Theorem of linear programming, if either a linear program or its dual has no feasible point, then the other one has no solution. Illustrate this assertion with an example.

Chapter 17

In a manufacturing process, the final product has a requirement that it must weigh exactly 150 pounds. The two raw materials used are \(\mathrm{A}\), with a cost of \(\$ 4\) per unit and \(\mathrm{B}\), with a cost of \(\$ 8\) per unit. At least 14 units of \(\mathrm{B}\) and no more than 20 units of A must be used. Each unit of A weighs 5 pounds; each unit of \(\mathrm{B}\) weighs 10 pounds. How much of each type of raw material should be used for each unit of final product if we wish to minimize cost?

Chapter 17

Solve the following linear programming problem: Maximize \(\quad 6 \mathrm{~L}_{1}+11 \mathrm{~L}_{2}\) subject to: \(\quad 2 \mathrm{~L}_{1}+\mathrm{L}_{2} \leq 104\) \(\mathrm{L}_{1}+2 \mathrm{~L}_{2} \leq 76\) and \(L_{1} \geq 0, L_{2} \geq 0\)

Chapter 17

A businessman needs 5 cabinets, 12 desks, and 18 shelves cleaned out. He has two part time employees Sue and Janet. Sue can clean one cabinet, three desks and three shelves in one day, while Janet can clean one cabinet, two desks and 6 shelves in one day. Sue is paid \(\$ 25\) a day, and Janet is paid \(\$ 22\) a day. In order to minimize the cost how many days should Sue and Janet be employed?

The first learning app that truly has everything you need to ace your exams in one place.

- Flashcards & Quizzes
- AI Study Assistant
- Smart Note-Taking
- Mock-Exams
- Study Planner