Bakers ' Club is trying to raise funds by selling premium chocolate chip cookies in a school fair . The variable cost to make each cookie is P15.00 and it is being sold for P25.00 So far the organization has already shelled out P790.00 for the cookie sale A.Find the profit function P (x) where x represents the number of cookies sold Solve by following this: Profit = Total Revenue - Total Cost Total Revenue = Price per unit x quantity sold Total Cost = Total variable cost + fixed cost B.If 146 cookies were sold , how much is the total profit? C.How many cookies must be made and sold to break even? Break even point is the zero of P(x) D.How many cookie should be sold to gain a profit of P250,00 ?
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.
Bakers ' Club is trying to raise funds by selling premium chocolate chip cookies in a school fair . The variable cost to make each cookie is P15.00 and it is being sold for P25.00 So far the organization has already shelled out P790.00 for the cookie sale
A.Find the profit function P (x) where x represents the number of cookies sold
Solve by following this:
Profit = Total Revenue - Total Cost Total Revenue = Price per unit x quantity sold
Total Cost = Total variable cost + fixed cost
B.If 146 cookies were sold , how much is the total profit?
C.How many cookies must be made and sold to break even? Break even point is the zero of P(x)
D.How many cookie should be sold to gain a profit of P250,00 ?
This is the answers to my questions:
A. P(x) = 10x - 790
B. P670.00
C. 79 cookies
D. 104 cookies
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