Question

A company can make 12 printing presses for $78,600. It can make 19 printing presses for $82,380. Find the linear equation that models the cost to produce x printing presses. Use slope-intercept form

Answer 1

Answer:

$C(x) = 540x + 72120$

Step-by-step explanation:

Given

Cost = $78,600 when Printing Press = 12

Cost = $82,380 when Printing Press = 19

Required

Determine the linear equation

From the given parameters; Cost is a function of Printing Press

Represent Cost by C and Printing press by x;

This implies that C = f(x)

The given parameters can then be modeled as; $(x, C)$

$(x_1, C_1) = (12,78600)$

$(x_2, C_2) = (19,82380)$

The first step is to calculate the slope, m;

$m = \frac{C_1 - C_2}{x_1 - x_2}$

$m = \frac{78600 - 82380}{12 - 19}$

$m = \frac{-3780}{-7}$

$m = 540$

The linear equation can then be calculated using slope formula

$m = \frac{C- C_2}{x - x_2}$

Substitute 540 for m and $(x_2, C_2) = (19,82380)$

$540 = \frac{C- 82380}{x - 19}$

Multiply both sides by x - 19

$540 * (x-19)= \frac{C- 82380}{x - 19} * (x-19)$

$540 * (x-19)= C- 82380$

Open bracket

$540x - 10260 = C - 82380$

Add 82380 to both sides

$540x - 10260 + 82380= C - 82380 + 82380$

$540x - 10260 + 82380= C$

$540x + 72120= C$

$C = 540x + 72120$

Hence;

$C(x) = 540x + 72120$