HELP PLEASE!! DUE IN 3 DAYS!

Question

Price of watermelon: $51.00 per m^2

Price of grapes: $65.34 per m^2

Area of farm: 480m^2

Okay, so now all in all we have built our farm and found what to price each of our crops at. Now let’s find what amount of each crop to grow and find our profits.

Getting right into it, we have the following cost equations:

CW = $20.00 * W + $50.00 CG = $10.00 * G + $40.00

Where CW is the total cost of planting and growing Watermelons, CG is the total cost of planting and growing Grapes, W is the area of Watermelons planted, and G is the area of Grapes planted. Now that we know our cost, we can finally find our profits. Profit is equal to the price per unit area, multiplied by the area sold, subtracted by the total cost planting and growing them, or,

Profit = Price * Area - Cost

But at this point, we still don’t know the area of each crop in our field. But we do know a couple of things to figure it out. We know the total area of our farm, found in the first part. Which we can say is,

Area = G + W And we were also only given $1590 to plant the crops. So,

$1590.00= CW+CG

I’ll help you simplify this a bit, $1590.00=$20.00*W+$50.00+$10.00*G+$40.00

$1590.00=$20.00*W+$10.00*G+$90.00

So now we have enough information to solve for the areas of Watermelons and Grapes in your field. Here’s some room to do that.

Area of Watermelons to plant = 

Area of Grapes to plant =

Now that we know the area of each to be grown, we can finally stick those values into our Profit equation for W and G respectively.

Profit of the Crops =

Answer 1

Hi Hanie,

Price of Watermelon: $51/m²

Price of Grapes: $65.34/m²

Farm Area: 480 m²

Budget for Planting: $1590

CW = $20 * W + $50

CG = $10 * G + $40

Cost Equation:

1590 = 20 * W + 10 * G + 90

Solving for the summation of W & G, we get:

W + G = 480

This is our area constraint.

Now we have two equations:

1. 2 * W + G = 150
2. W + G = 480

Subtracting 2 from 1:

(2 * W + G) - (W + G) = 150 - 480

W = -330

***ERROR***

This is impossible, since the area of a crop cannot be negative. Therefore, the information provided in the problem is inconsistent. There is no valid solution, because the farm area and budget constraints contradict each other. To fix the problem, either the budget, costs, or total area must be different.

Hope this helps!!!

-Andrew Evans