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When the price for a color television is $\$ 240,$ the monthly sales for this item at a department store is 450. For each $\$ 5$ increase in price, the monthly sales fall by 5 units. How many color televisions should be sold to maximize monthly sales and what price should be changed to maximize sales?

$345, \$ 345$

Algebra

Chapter 1

Functions and their Applications

Section 6

Economic Functions

Functions

Campbell University

Oregon State University

McMaster University

University of Michigan - Ann Arbor

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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But the given problem, we have the price of a color television is $240,. And the monthly sales for this item is 450. So for each $5 increase in price, the monthly sales four x 5 units. So we want to know how many colour television should be sold to maximize monthly sales and what price should be changed to in order to maximize the sales. So if we know the prices to 40, the monthly sales um at a department store is for 50 we see that this is going to be A point on a graph for 50 2 40. Right? Then we see that as the prices increased by $5, the sales falls by five units. So as the price increases, so we would have 4 45 and two. Mhm. So we can see just based on those two points how the demand function will be decreasing. And we see that the the way to maximize it would be 345 units sold at $345.

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