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sveticcg [70]
3 years ago
9

A farmer is going to divide her 30 acre farm between two crops. Seed for crop A costs $5 per acre. Seed for crop B costs $10 per

acre. The farmer can spend at most $200 on seed. If crop B brings in a profit of $50 per acre, and crop A brings in a profit of $160 per acre, how many acres of each crop should the farmer plant to maximize her profit
Mathematics
1 answer:
jenyasd209 [6]3 years ago
3 0

Answer:

30 acres of A

0 acres of B

Step-by-step explanation:

On forming the equations we get

Acres = A+B \leq 30  .............(1)

Seed = 5A + 10B \leq 200 ...........(2)

Profit = 160A+50B

Upon rearranging this we get

A= 30-B     sing equation (1)

A=40-2B   using equation (2)

 On plotting these inequalities on the cartesian planes we will get the following points of intersection (0,20) (20,30) (30,0)

Now using these coordinates (A,B) to get Maximum profit

P= $1000 for (0,20)

P=$4700 for (20,30)

P= $4800 for (30,0)

clearly for (30,0) we will get the maximum profit on the crops

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Answer:

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case b) x^{2}=-10y ----> open down

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Step-by-step explanation:

we know that

1) The general equation of a vertical parabola is equal to

y=a(x-h)^{2}+k

where

a is a coefficient

(h,k) is the vertex

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If a<0 ----> the parabola open downward and the vertex is a maximum

2) The general equation of a horizontal parabola is equal to

x=a(y-k)^{2}+h

where

a is a coefficient

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If a>0 ----> the parabola open to the right

If a<0 ----> the parabola open to the left

Verify each case

case a) we have

x^{2}=3y

so

y=(1/3)x^{2}

a=(1/3)

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The parabola open up

case b) we have

x^{2}=-10y

so

y=-(1/10)x^{2}

a=-(1/10)

a

therefore

The parabola open down

case c) we have

y^{2}=-2x

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x=-(1/2)y^{2}

a=-(1/2)

a

therefore

The parabola open to the left

case d) we have

y^{2}=6x

so

x=(1/6)y^{2}

a=(1/6)

a>0

therefore

The parabola open to the right

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