Course:MATH110/Archive/2010-2011/003/Teams/Aargau/Homework 11

The marginal cost is the cost of producing one more unit. The data that is given to us is: It will cost 100 dollars to create 20 units, and it will cost 7 dollars per unit if you want to create more. In this situation, we are given two pieces of information: one point on our graph (20,100) and the slope of the linear function, which is 7. We can find the equation.
y-y1=m(x-x1)
y-100=7(x-20)
y-100=7x-140
y=7x-40
We can find how much it would cost to produce 150 units using this equation.
Y=7(150)-40
Y=1050-40
Y=1010
It will cost 1010 dollars to produce 150 units. Because this is a linear equation, the average cost of each unit as production increases remains constant. We can find other models that show other things about the average cost as production increases. We can do this by imagining that on the graphs, the y-axis is the average cost and the x-axis is the quantity produced. In a situation where the average cost remains constant as production increases, the function would have to be linear and the slope 0. An example is y=5 or y=9 If the average cost diminishes as production increases, it means that the slope is negative, or that the marginal cost is negative. An example would be y=-7x-40 If the average cost is increasing, we need a positive slope. An example would be y=10x+5. It’s important to note that these functions are plotted where the y-axis is average cost and the x-axis is quantity produced. In a situation when a company reaches economies of scale, the equation will have to have a negative slope, similar to a problem that was explored earlier.