Question

hi how do i do this problem?Producers of a certain brand of refrigerator will make 1600 refrigerators available when the unit price is $370. At a unit price of $420, 5600 refrigerators will be marketed. Find the equation relating the unit price p of a refrigerator to the quantity supplied x if the equation is known to be linear.p = How many refrigerators will be marketed when the unit price is $470? refrigeratorsWhat is the lowest price at which a refrigerator will be marketed?

Answer 1

In order to find the equation relating the unit price p and the quantity x, let's use the slope-intercept form of the linear equation:

`p=mx+b`

Where m is the slope and b is the y-intercept.

To find the value of m and b, let's use the ordered pairs (x, p) given in the question.

The given points are (1600, 370) and (5600, 420), so we have:

`\begin{gathered} (1600,370)\colon \\ 370=1600m+b \\ (5600,420)\colon \\ 420=5600m+b \end{gathered}`

Subtracting the first equation from the second one, we have:

`\begin{gathered} 420-370=5600m+b-(1600m+b) \\ 50=4000m \\ m=0.0125 \\ \\ 370=1600\cdot0.0125+b \\ b+20=370 \\ b=350 \end{gathered}`

Therefore the equation is p = 0.0125x + 350.

For a unit price of $470, we have:

`\begin{gathered} 470=0.0125x+350 \\ 0.0125x=120 \\ x=9600 \end{gathered}`

The lowest price is given by x = 1 (at least one refrigerator will be marketed), so:

`\begin{gathered} p=0.0125\cdot1+350 \\ p=350.01 \end{gathered}`