Question

Rienzi Farms grows sugar cane and soybeans on its 500 acres of land. An acre of soybeans brings a $1000 contribution to overhead and profit; an acre of sugar cane has a contribution of $2000. Because of a government program no more than 200 acres may be planted in soybeans. During the planting season 1200 hours of planting time will be available. Each acre of soybeans requires 2 hours, while each acre of sugar cane requires 5 hours. The company seeks maximum contribution (profit) from its planting decision.

a. Formulate the problem as a linear program.

b. Solve using the Lingo software and include the output

Please use excel where applicable! Thanks!!!

Answer 1

(a)

Formulation

Maximize 1000X + 2000Y

ST

X + Y <= 500

X <= 200

2X + 5Y <= 1200

X, Y >= 0

Here, X = acre of soybeans and Y = acre of sugar cane

(b)

Since you asked for excel even though there's lindo mentioned, I'm proceeding with excel, If you wanted lingo output, please let me know in the comments. Thank you.

Initial excel formulation:

Formulas:

Solver constraints:

Clicking solve, we get

X = 200, Y = 160 and Z = 520000

PLEASE LEAVE A LIKE. IT REALLY HELPS ME A LOT. THANK YOU!!!