Question

A company is planning to set up a new manufacturing plant for giant inflatable beach balls and believe the costs follow a linear model. The cost analysts estimate the cost of producing 10,000 beach balls to be $587,500 and the cost of producing 50,000 beach balls to be $717,500

Answer 1

The cost(y) of producing x number of balls is given by the linear model y = 3.25x + 685000

Linear equation

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change (slope) and b is the y intercept.

Let y represent the cost of producing x number of beach balls.

Using the point (10000, 587500) and (50000, 717500):

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-717500=\frac{717500-587500}{50000-10000} (x-10000)\\\\y=3.25x+685000$

The cost(y) of producing x number of balls is given by the linear model y = 3.25x + 685000

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