Mathematics, 23.10.2019 08:50 makoa

The grower has 250 acres of land available to raise 2 crops, apples and peaches. it takes 1 day to fertilize an acre of apples and two days to fertilize 1 acre of peaches. there are 240 days a year available for fertilizing. find the number acres of each fruit that should be planted to maximize profit. assuming that the profit is $120 per acre of apples and $215 per acre of peaches. find the constants.

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Answer from: johnisawesome999

The maximum profit will be $28,800 when 240 acres go for apples and 0 acres go for peaches

Step-by-step explanation:

Let x be the number of acres with apples and y be the numbere of acres with peaches. Note that $x\ge 0, \ y\ge 0.$

The grower has 250 acres of land available, then

$x+y\le 250$

It takes 1 day to fertilize an acre of apples, so it takes x days to fertilize x acres of apples.

It takes 2 days to fertilize 1 acre of peaches, so it takes 2y days to fertilize y acres of peaches.

There are 240 days a year available for fertilizing, so

$x+2y\le 240$

The profit is $120 per acre of apples and $215 per acre of peaches, then the total profit is

P=120x+215y

We get the function P=120x+215y which must maximized using restrictions

$\left\{\begin{array}{l}x\ge 0\\y\ge 0\\x+y\le 250\\ x+2y\le 240\end{array}\right.$

Show the solution set of this system of inequalities graphically.

The maximum profit can be at the vertices of this region:

$P(0,120)=120\cdot 0+215\cdot 120=\$25,800\\ \\P(240,0)=120\cdot 240+215\cdot 0=\$28,800$

The maximum profit will be $28,800 when 240 acres go for apples and 0 acres go for peaches

The grower has 250 acres of land available to raise 2 crops, apples and peaches. it takes 1 day to f

Answer from: Quest

sum= when you add is how much the whole amount is

distance= when you use angles and it means how far it goes

step-by-step explanation:

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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