A company manufactures x units of Product A and y units of Product 8, on two machines, I and II. The company will realize a profit of $4.50/unit of Product A and a profit of $4/unit of Product B. Manufacturing 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. Manufacturing 1 unit of Product 8 requires 9 min on Machine 1 and 4 min on Machine and 3 hr of time available on Machine II in each work shift. (a) How many units of each product should be produced in each shift to maximize the company's profit? The maximum is P-t (1)-(). (b) Suppose P = cx + 4y. Find the range of values that the contribution to the profit of 1 unit of Product A, the coefficient c of x, can assume without changing the optimal solution. Loy seven ses

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...
icon
Related questions
Question
100%
A company manufactures x units of Product A and y units of Product B, on two machines, I and II. The company will realize a profit of $4.50/unit of Product A and a profit of $4/unit of Product B. Manufacturing 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. Manufacturing 1 unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of time available on Machine I
and 3 hr of time available on Machine II in each work shift.
(a) How many units of each product should be produced in each shift to maximize the company's profit?
The maximum is P =
at (x, y) = (
(b) Suppose P = cx + 4y. Find the range of values that the contribution to the profit of 1 unit of Product A, the coefficient c of x, can assume without changing the optimal solution.
scs
(c) Find the range of values (in hours) that the resource associated with the time constraint on Machine I can assume.
s (resource) s
(d) Find the shadow price for the resource associated with the time constraint on Machine I.
Transcribed Image Text:A company manufactures x units of Product A and y units of Product B, on two machines, I and II. The company will realize a profit of $4.50/unit of Product A and a profit of $4/unit of Product B. Manufacturing 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. Manufacturing 1 unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of time available on Machine I and 3 hr of time available on Machine II in each work shift. (a) How many units of each product should be produced in each shift to maximize the company's profit? The maximum is P = at (x, y) = ( (b) Suppose P = cx + 4y. Find the range of values that the contribution to the profit of 1 unit of Product A, the coefficient c of x, can assume without changing the optimal solution. scs (c) Find the range of values (in hours) that the resource associated with the time constraint on Machine I can assume. s (resource) s (d) Find the shadow price for the resource associated with the time constraint on Machine I.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax