19. A manufacturer has RM8,000 to spend on the development and promotion of a new product. It is estimated that if x thousand ringgit is spent on development and y thousand ringgit is spent on promotion, sales will be approximately 1(x,y) = 50 x ™y * units. How much money should the manufacturer allocate to development and how much to promotion to maximize sales?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
icon
Related questions
Topic Video
Question
18.
A manufacturer who is a monopolist makes two types of lamps. From experience the
manufacturer has determined that if x lamps of the first type and y lamps of the second
type are made, they can be sold at for (100 - 2x) dollars each and (125 – 3 y) dollars
each respectively. The cost of manufacturing x lamps of the first type and y lamps of the
second type is (12 x +11 y + 4 xy ) dollars. How many lamps of each type should be
produced in order to realize the greatest profit, and what is the greatest profit?
19.
A manufacturer has RM8,000 to spend on the development and promotion of a new
product. It is estimated that if x thousand ringgit is spent on development and y
thousand ringgit is spent on promotion, sales will be approximately 1 (x, y) = 50 x "y"
units. How much money should the manufacturer allocate to development and how
much to promotion to maximize sales?
20.
A closed rectangular box with a volume V cm. The cost of materials used in the box is
a sen/cm? for the top and the bottom, b sen/cm² for front and back, and c sen/cm²
for the remaining sides. Find the dimensions of the box so that the cost of materials is
minimized.
Transcribed Image Text:18. A manufacturer who is a monopolist makes two types of lamps. From experience the manufacturer has determined that if x lamps of the first type and y lamps of the second type are made, they can be sold at for (100 - 2x) dollars each and (125 – 3 y) dollars each respectively. The cost of manufacturing x lamps of the first type and y lamps of the second type is (12 x +11 y + 4 xy ) dollars. How many lamps of each type should be produced in order to realize the greatest profit, and what is the greatest profit? 19. A manufacturer has RM8,000 to spend on the development and promotion of a new product. It is estimated that if x thousand ringgit is spent on development and y thousand ringgit is spent on promotion, sales will be approximately 1 (x, y) = 50 x "y" units. How much money should the manufacturer allocate to development and how much to promotion to maximize sales? 20. A closed rectangular box with a volume V cm. The cost of materials used in the box is a sen/cm? for the top and the bottom, b sen/cm² for front and back, and c sen/cm² for the remaining sides. Find the dimensions of the box so that the cost of materials is minimized.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Optimization
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
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