Question

how do i set this up...i need help in the set up...

In deciding whether or not to set up a new manufacturing plant, analysts for a popcorn compnay ave decided that a linear function is a reasonable estimation for the total cost c(x)in dollars to produce x bags of microwave popcorn. They estimate the cost to produce 10,000 bags as $5480 and the cost to produce 15,000 bags as $7780 Find the marginal cost of thebags of microwave popcorn to be produce in this plant.

The marginal cost per five thousand is 7780-5480. So the marginal cost per bag is....

SO THE 7780-5480 = 2300
BAGS: 15000-10000=5000

wHAT DO I DO FROM HERE

Answer 1

"Linear function" means straight line with price on the Y axis and bags on the X axis.

So "10,000 bags as $5480" makes up the point (10000, 5480) and "15,000 bags as $7780" makes the point (15000, 7780).

Marginal cost of bags of microwave popcorn is the SLOPE of the line. (Dndubins is wrong. Marginal product is not the y-intercept. It's the slope. The y-intercept is the fixed cost.) In this case, the slope would be the change in cost for every increase in 1 bag of popcorn.

Slope = (Y1-Y2) / (X1-X2) so just plug the points into this equation

(7780 - 5480) / (15000 - 10000) = 2300 / 5000 = 0.46

Therefore, the marginal cost of each bag is $0.46.

You can double check your work by solving for the y-intercept and getting the entire equation of the linear function. The slope-intercept form of the line is y = mx+b so just plug in (10000, 5480).
5480 = 0.46 (10,000) + b

Multiply 0.46 by 10,000
5480 = 4600 + b

Subtract 4600 from both sides
b = 880

Therefore, the equation of the line is Y = 0.46X + 880.

Plug in the second point (15000, 7780) to see if it works
7780 = 0.46(15000) + 880

Simplify the right side:
7780 = 7780

So you know the marginal cost does in fact equal $0.46