Maximizing Profits The weekly demand for the Pulsar 40-in. high-definition television is given by the demand equation p = −0.06x + 549    (0 ≤ x ≤ 12,000) where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated with manufacturing these sets is given by   C(x) = 0.000002x3 − 0.01x2 + 400x + 80,000   where C(x) denotes the total cost incurred in producing x sets. Find the level of production that will yield a maximum profit for the manufacturer. Hint: Use the quadratic formula. (Round your answer to the nearest whole number.)   ____________ units

Q: (A) C =D (Simplify your answer. U your answer.)

A: We have to find the total daily cost C of producing x golf clubs.

Q: 30 P= √I droppings" can be modeled by,

A: Given the demand model : p=30x The cost - model is : C=2.1x-142 where x is in tons. We need to find…

Q: The demand equation for a quantity q of a product, in hundreds, at price p, in million rands, is p =…

A:

Q: Assume that the relationship between price p and demand x is linear. Express p as a function of x…

A: P= $2.5, Q = 2750   P = $2.80, Q = 2600   Fixed cost = $4450.40   VC = $1.34   Lets first find out…

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.