Question

1. pepper farmer in New Mexico can grow a combination of jalapenos, habaneros, and poblanos. He is endowed with 350 acres of land, 500 hours of labor, and 300 bags of fertilizer. Additionally, they have $45,000 as an operating budget (meaning they can’t spend more than that prior to selling the peppers). The table below provides the relevant production information.

	Labor (hrs/acre)	Cost ($/acre)	Fertilizer (bags/acre)	Yields (bu/acre) Prices ($/bushel)
Plowing (pl)	.75	4
Plant jalapenos (pj)	.40	110	.70
Plant habaneros (ph)	.45	75	.75
Plant poblanos (pp)	.35	95	.70
Harvest jalapenos (hj)	.30	20		100
Harvest habaneros (hh)	.45	20		95
Harvest poblanos (hp)	.40	30		85
Sell jalapenos (sj)				$4.00
Sell habaneros (sh)				$3.00
Sell poblanos (sp)				$5.00

1. Please use the table on the next page to express the LP problem. I have provided you with the decision variables, so you need to express the objective function and ALL constraints in table form.

Answer 1

Assume that the different crops are planted according to the following variables:

Japapenos on x acres

Habaneros on y acres

Poblanos on z acres

Since the yield is: 100 bushels, 95 bushels and 85 bushels per acre for these crops and their prices are $4 per bushel, $3 per bushel and $5 per bushel, the objective function is

Maximize: $400x + $285y + $425z

(yield per acre times price per bushel times the quantity)

The 4 constraints are as follows:

1. Land: x + y + z <= 350

2. Labour: (0.75+0.40+0.30)x + (0.75+0.45+0.45)y + (0.75+0.35+0.40)z <=500

1.45x + 1.65y + 1.50z <= 500

Plowing 0.75 per acre for each crop + Planting for each crop + Harvesting for each crop

3. Fertilizer: 0.70x + 0.75y + 0.70z <= 300

4. Cost: ($4+110+20)x + ($4+75+20)y + ($4+95+30)z <= $45000

134x + 99y + 129z <= 45000

Plowing $4 per acre for each crop + Planting for each crop + Harvesting for each crop