Answer:
The animal farm should buy 1.775 bags of soybeans and 1.575 bags of oats
[tex]Cost = 51.275[/tex]
Step-by-step explanation:
The given parameters can be summarized as:
[tex]\begin{array}{cccc}{} & {x} & {y} & {Total} & {Protein} & {70} & {21} & {168} &{Fats}& {9} & {7} & {27} & {Minerals} & {7} & {1} & {14}& {Cost} & {21} & {7} & {} \ \end{array}[/tex]
Where: x = Soybeans and y = Oats.
So, the system of equations are:
[tex]70x + 21y = 168[/tex]
[tex]9x +7y = 27[/tex]
[tex]7x + y = 14[/tex]
[tex]Cost = 21x + 7y[/tex]
The best way to solve this, is using graph
Plot the following equations on a graph, and get the points of intersection:
[tex]70x + 21y = 168[/tex]
[tex]9x +7y = 27[/tex]
[tex]7x + y = 14[/tex]
From the attached graph, we have:
[tex](x_1,y_1) = (1.636,2.545)[/tex]
[tex](x_2,y_2) = (1.775,1.575)[/tex]
[tex](x_3,y_3) = (2.023,1.256)[/tex]
Substitute each of the values of x's and y's in the cost function to get the minimum cost:
[tex]Cost = 21x + 7y[/tex]
[tex](x_1,y_1) = (1.636,2.545)[/tex]
[tex]Cost = 21 * 1.636 + 7 * 2.545[/tex]
[tex]Cost = 52.171[/tex]
[tex](x_2,y_2) = (1.775,1.575)[/tex]
[tex]Cost = 21 * 1.775 + 7 * 1.575[/tex]
[tex]Cost = 48.3[/tex]
[tex](x_3,y_3) = (2.023,1.256)[/tex]
[tex]Cost = 21 * 2.023 + 7 * 1.256[/tex]
[tex]Cost = 51.275[/tex]
The values of x and y that gives the minimum cost is:
[tex](x_2,y_2) = (1.775,1.575)[/tex]
and the minimum cost is:
[tex]Cost = 48.3[/tex]
Hence, the animal farm should buy 1.775 bags of soybeans and 1.575 bags of oats
