market study determined that for each unit a good is sold Hi-Fi electronics the unit price of it falls by $ 380 [MU]. Yes when not units of this good are sold, the unit price is $ 8,360 [MU]., determine: a) The model or function that relates the unit price X of the good in relation to the quantity sold and, knowing that it is linear. b) How many units of the good must be sold, so that the unit price is $ 2660 [UM]. c) How many units must be sold so that each one is exactly free? one of them? d) Using a graph, determine the domain and economic path of the function of unit price

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 60E
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market study determined that for each unit a good is sold Hi-Fi electronics the unit price of it falls by $ 380 [MU]. Yes when not units of this good are sold, the unit price is $ 8,360 [MU]., determine:

a) The model or function that relates the unit price X of the good in relation to the quantity sold and, knowing that it is linear.

b) How many units of the good must be sold, so that the unit price is $ 2660 [UM].

c) How many units must be sold so that each one is exactly free? one of them?

d) Using a graph, determine the domain and economic path of the function of unit price

Expert Solution
Step 1

Part (a)

P0 = Price when no unit is sold = 8,360

Rate of decline of the price = m = 380

Hence, P(Q) = P0 - mQ

Or, P(Q) = 8,360 - 380Q

where Q is the number of units sold

Step 2

Part (b)

We have to find Q such that P(Q) = 2,660

Hence, 2,660 = 8,360 - 380Q

Hence, Q = (8,360 - 2,660) / 380 = 15

Part (c)

We have to find Q such that P(Q) = 0

Hence, 8,360 - 380Q = 0

Hence, Q = 8,360 / 380 = 22

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