A manufacturer of 24-hr variable timers, has a monthly fixed cost of $42,000 and a production cost of $5 for each timer manufactured. The units sell for $12 each. (a) Graph the cost and revenue functions. (Use rays with closed endpoints along the y-axis.) (b) Find the break-even point. (x, y) = (c) Graph the profit function. (Use a ray with closed endpoint along the y-axis.) (d) At what point does the graph of the profit function cross the x-axis? (x, y) = The quantity demanded x of a certain brand of DVD player is 3000/week when the unit price p is $485. For each decrease in unit price of $20 below $485, the quantity demanded increases by 250 units. The suppliers will not market any DVD players if the unit price is $350 or lower. But at a unit price of $525, they are willing to make available 2500 units in the market. The supply equation is also known to be linear. (a) Find the demand equation.p(x) = (b) Find the supply equation.p(x) = (c) Find the equilibrium quantity and the equilibrium price.
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 of 24-hr variable timers, has a monthly fixed cost of $42,000 and a production cost of $5 for each timer manufactured. The units sell for $12 each.
p(x) =
p(x) =
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