a) Suppose the farmer makes a profit of $45 per acre of celery and $50 per acre of lettuce. Write the profit function, determine how many acres of celery and lettuce he should plant to maximize profit, and state the maximum profi
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
A farmer has 300 acres on which to plant two crops, celery and
lettuce. Each acre of celery costs $250 to plant and tend,
and each acre of lettuce costs $300 to plant and tend. The
farmer has $81,000 available to cover these costs.
a) Suppose the farmer makes a profit of $45 per acre of
celery and $50 per acre of lettuce. Write the profit
function, determine how many acres of celery and lettuce he should plant to maximize profit, and state the
maximum profit. (Hint: Since the graph of the profit
function is a plane, you will not need to check the
interior for possible critical points.)
b) Suppose the farmer’s profit function is instead P(x, y) = - x2 - y2 + 600y- 75,000. Assuming the same constraints, how many acres of celery and
lettuce should he plant to maximize profit, and what
is that maximum profit?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
