1. The price-demand equations x = f(p, q) and y = g(p, q) represent the num- ber of units demanded of products A and B, respectively, at a price p for 1 unit of product A and a price q for 1 unit of product B. Below are examples of weekly price demand equations for A and B: x = f(p, q) = 800 – 0.9p² + 0.8q² Product A y = g(p, q) = 1500 +0.4p² – 0.3q² Product B (a) Find a function R (in terms of two independent variables) to denote the total revenue (in pesos) from selling both products. Find R,(10,2) and interpret the results. (b) In general, when two products, A and B, tend to be consumed or used together, the products are said to be complementary. Mathematically, this means that f,(p,q) < 0 and g,(p, q) < 0 should both be true. Give an example of two products that are complementary. (c) In general, A and B are said to be competitive (substitute) products if fa(p, q) > 0 and gp(p, q) > 0. Explain what these inequalities mean. (d) If neither conditions in (b) nor (c) are met, the products are neither com- plementary nor competitive. Use the tests above to determine whether the products in the given examples are complementary, competitive, or

1. The price-demand equations x = f(p, q) and y = g(p, q) represent the num- ber of units demanded of products A and B, respectively, at a price p for 1 unit of product A and a price q for 1 unit of product B. Below are examples of weekly price demand equations for A and B: x = f(p, q) = 800 – 0.9p² + 0.8q² Product A y = g(p, q) = 1500 +0.4p² – 0.3q² Product B (a) Find a function R (in terms of two independent variables) to denote the total revenue (in pesos) from selling both products. Find R,(10,2) and interpret the results. (b) In general, when two products, A and B, tend to be consumed or used together, the products are said to be complementary. Mathematically, this means that f,(p,q) < 0 and g,(p, q) < 0 should both be true. Give an example of two products that are complementary. (c) In general, A and B are said to be competitive (substitute) products if fa(p, q) > 0 and gp(p, q) > 0. Explain what these inequalities mean. (d) If neither conditions in (b) nor (c) are met, the products are neither com- plementary nor competitive. Use the tests above to determine whether the products in the given examples are complementary, competitive, or

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Description: 1. The price-demand equations x = f(p, q) and y = g(p, q) represent the num-ber of units demanded of products A and B, respectively, at a price p for 1unit of product A and a price q for 1 unit of product B. Below are examplesof weekly price demand

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

Topic Video

Question

1. The price-demand equations x = f(p, q) and y = g(p, q) represent the num-
ber of units demanded of products A and B, respectively, at a price p for 1
unit of product A and a price q for 1 unit of product B. Below are examples
of weekly price demand equations for A and B:
x = f(p, q) = 800 – 0.9p² + 0.8q²
Product A
y = g(p, q) = 1500 + 0.4p² – 0.3q²
Product B
(a) Find a function R (in terms of two independent variables) to denote
the total revenue (in pesos) from selling both products. Find R,(10,2)
and interpret the results.
(b) In general, when two products, A and B, tend to be consumed or used
together, the products are said to be complementary. Mathematically,
this means that fa(p, q) < 0 and g,(p, q) < 0 should both be true. Give
an example of two products that are complementary.
(c) In general, A and B are said to be competitive (substitute) products if
fa(p, q) > 0 and gp(p, q) > 0. Explain what these inequalities mean.
(d) If neither conditions in (b) nor (c) are met, the products are neither com-
plementary nor competitive. Use the tests above to determine whether
the products in the given examples are complementary, competitive, or
neither.

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