A manufacturer has a monthly fixed cost of $60,000 and a production cost of S10 for each unit produced. The product sells for $15/unit. What is the cost function? What is the revenue function? What is the profit function?
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
- A manufacturer has a monthly fixed cost of $60,000 and a production cost of S10 for each unit produced. The product sells for $15/unit.
- What is the cost function?
- What is the revenue function?
- What is the profit function?
- Compute the profit (loss) corresponding to production levels of 10,000 and 14,000 units.
- How many units should the firm produce in order to realize a minimum monthly profit of $5000?
- How many units must be sold to break even?
- There is no demand for a certain make of one-time use camera when the unit price is $ 12. However, when the unit price is $ 8, the quantity demanded is 8000/week.
The supplier will not market any cameras if the unit price is $ 2 or lower. At $ 4/camera, however, the manufacturer will make available 5000 cameras/week.
Given that both the supply and demand equations are linear:
- Determine the associated linear demand function
- Determine the linear supply function.
- At what price should the camera be sold so that there is neither a surplus nor a shortage?
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