POTTERY COMPANY EMPLOYS SKILLED ARTISANS TO PRODUCE CLAY BOWLS AND MUGS. THE TWO PRIMARY RESOURCES ARE SPECIAL POTTERY CLAY AND SKILLED LABOR. GIVEN THIS LIMITED RESOURCES, THE COMPANY DESIRES TO KNOW HOW MANY BOWLS AND MUGS TO PRODUCE EACH DAY IN ORDER TO MAXIMIZE THE PROFIT. Labor (hr/unit) Clay (lb/unit) Bowl Mug THERE ARE 10 HOURS OF LABOR AND 30 POUNDS OF CLAY AVAILABLE EACH DAY FOR PRODUCTION. THE UNIT PROFITS OF EACH BOWL AND MUG ARE $30 AND $10, RESPECTIVELY. (A) DEFINE DECISION VARIABLES. (B) WRITE A SUITABLE LP PROBLEM FORMULATION AND SOLVE IT GRAPHICALLY. (c) WRITE THE DUAL PROBLEM OF PART (x). (D) SOLVE PART (C) USING THE COMPLEMENTARY SLACKNESS.
POTTERY COMPANY EMPLOYS SKILLED ARTISANS TO PRODUCE CLAY BOWLS AND MUGS. THE TWO PRIMARY RESOURCES ARE SPECIAL POTTERY CLAY AND SKILLED LABOR. GIVEN THIS LIMITED RESOURCES, THE COMPANY DESIRES TO KNOW HOW MANY BOWLS AND MUGS TO PRODUCE EACH DAY IN ORDER TO MAXIMIZE THE PROFIT. Labor (hr/unit) Clay (lb/unit) Bowl Mug THERE ARE 10 HOURS OF LABOR AND 30 POUNDS OF CLAY AVAILABLE EACH DAY FOR PRODUCTION. THE UNIT PROFITS OF EACH BOWL AND MUG ARE $30 AND $10, RESPECTIVELY. (A) DEFINE DECISION VARIABLES. (B) WRITE A SUITABLE LP PROBLEM FORMULATION AND SOLVE IT GRAPHICALLY. (c) WRITE THE DUAL PROBLEM OF PART (x). (D) SOLVE PART (C) USING THE COMPLEMENTARY SLACKNESS.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
A Pottery Company employs skilled artisans to produce clay
bowls and mugs. The two primary resources are special pottery clay and skilled labor.
Given this limited resources, the company desires to know how many bowls and mugs to
produce each day in order to maximize the profit.
Labor (hr/unit) Clay (lb/unit)
Bowl 1 6
Mug 2 3
There are 10 hours of labor and 30 pounds of clay available each day for production. The
unit profits of each bowl and mug are $30 and $10, respectively.
(a) Define decision variables.
(b) Write a suitable LP problem formulation and solve it graphically.
(c) Write the dual problem of Part (b).
(d) Solve Part (c) using the complementary slackness.
Transcribed Image Text:**Pottery Company employs skilled artisans to produce clay bowls and mugs. The two primary resources are special pottery clay and skilled labor. Given this limited resources, the company desires to know how many bowls and mugs to produce each day in order to maximize the profit.**
| | Labor (hr/unit) | Clay (lb/unit) |
|---------------|-----------------|----------------|
| Bowl | 1 | 6 |
| Mug | 2 | 3 |
There are 10 hours of labor and 30 pounds of clay available each day for production. The unit profits of each bowl and mug are $30 and $10, respectively.
(a) Define decision variables.
(b) Write a suitable LP problem formulation and solve it graphically.
(c) Write the dual problem of Part (b).
(d) Solve Part (c) using the complementary slackness.
Transcribed Image Text:**Pottery Company Problem**
A Pottery Company employs skilled artisans to produce clay bowls and mugs. The two primary resources are special pottery clay and skilled labor. Given these limited resources, the company desires to know how many bowls and mugs to produce each day in order to maximize the profit.
| | Labor (hr/unit) | Clay (lb/unit) |
|---------------|-----------------|----------------|
| Bowl | 1 | 6 |
| Mug | 2 | 3 |
There are 10 hours of labor and 30 pounds of clay available each day for production. The unit profits of each bowl and mug are $30 and $10, respectively.
**(a) Define decision variables.**
**(b) Write a suitable LP problem formulation and solve it graphically.**
**(c) Write the dual problem of Part (b).**
**(d) Solve Part (c) using the complementary slackness.**
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