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
"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
To find the marginal cost per bag of microwave popcorn, you would divide the marginal cost per five thousand bags (which is $2300) by the number of bags in that quantity (which is 5000). This will give you the marginal cost per bag.
So, you can calculate the marginal cost per bag using the following formula:
Marginal Cost per bag = Marginal Cost per 5000 bags / Number of bags in that quantity
Substituting the values, you get:
Marginal cost per bag = $2300 / 5000
Calculating this, you will find that the marginal cost per bag of microwave popcorn in this plant is $0.46.