Convert The Function

Algebra Level pending

XYZ, inc. produces widgets at a cost of $12 a widget. After analyzing the demand for their widgets at various price levels, they have come up with the following function to model the demand at each price level:

$D(x) = -200x+7000$

How can XYZ, Inc. convert the function $D(x)$ into the function $E(x)$ that will model the cost-of-goods sold at each price level?

Multiply the function D(x) by the cost of a widget ($12). Add to the function D(x) the cost of a widget ($12). Not enough information. Divide the function D(x) by the cost of a widget ($12).

2 solutions

Hung Woei Neoh
Jun 9, 2016

$E(x)$ , the cost-of-goods functions, is actually the total cost of all units sold at a particular price level.

We know that: Total cost = Cost per unit $\times$ Number of units sold

Notice that $D(x)$ , the demand function is actually the function representing the number of units sold

Therefore,

$E(x) = 12 \times D(x)$

The answer is $\boxed{\text{Multiply the function D(x) by the cost of a widget (\$12)}}$

Justin Malme
Jun 9, 2016

Multiply the function by the cost of a widget ($12).

$D(x) = -200x+7000$

$E(x) = 12(-200x+7000) = -2400x+84000$

Convert The Function

2 solutions

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