Fertilizer Problem

A farmer needs to fertilize a field. Two brands of fertilizer, Super$-$gro and Crop$-$quick,

have different amount of nitrogen and phosphate, and different costs:

$$ A bag of Super$-$gro has $2$ lb$.$ of nitrogen, $4$ lb$.$ of phosphate, and costs $$6.$

$$ A bag of Crop$-$quick has $4$ lb$.$ of nitrogen, $3$ lb$.$ of phosphate, and costs $$3.$

The field requires at least $16$ lb$.$ of nitrogen and at least $24$ lb$.$ of phosphate. The farmer wants to know

how many bags of each fertilizer to use in order to minimize the total cost.

$1.$ Formulate an LP model for this problem. $($Make sure your LP model includes: definitions of

decision variables, an objective, constraints, and bounds on variables.$)$

$2.$ Solve the problem using the graphical method.

$3.$ Write the optimal solution and the optimal objective function value.

$4.$ Write an interpretation of the optimal solution and the optimal objective function value.

$5.$ Is the feasible region unbounded?

$6.$ Is the problem unbounded?

$7.$ How many pounds of nitrogen and phosphate are provided by the optimal solution? Are they

equal to minimum requirements?