pepper farmer in New Mexico can grow a combination of jalapenos, habaneros, and poblanos. He is...

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

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.

Solutions

Expert Solution

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

Rahul Sunny answered 2 years ago

Next > < Previous

Related Solutions

A farmer has decided to use a new additive to grow his crops. He divided his...

A farmer has decided to use a new additive to grow his crops. He divided his farm into 10 plots and kept records of the corn yield (in bushels) before and after using the additive. The before (first row) and after (second row) results from the 10 different plots are shown below. Corn Yield Before 9 9 8 7 6 8 5 9 10 11 After 10 9 9 8 7 10 6 10 10 12 You wish to test...

A farmer must decide what crops to grow on a 300-hectare tract of land. He can...

A farmer must decide what crops to grow on a 300-hectare tract of land. He can grow oats, wheat, or barley, which yield 50, 100 and 80 kg/hectare (respectively) and sell for $1.00, $0.80, and $0.60 per kg (respectively). Production costs (fertilizer, labor, etc.) are $40, $50, and $40 per hectare for growing oats, wheat and barley, respectively. Government regulations restrict the farmer to a maximum of 150 hectares of wheat and his crop rotation schedule requires that he plants...

A farmer has 1000 acre of land on which he can grow corn, wheat and soyabeans....

A farmer has 1000 acre of land on which he can grow corn, wheat and soyabeans. Each acre of corn cost Rs. 100 for preparation, requires 7 man days of work and yields a profit of Rs. 30. An acre of wheat cost Rs. 120 for preparation, requires 10 man days of work and yields a profit of Rs. 40. An acre of soyabeans cost Rs. 70 to prepare, requires 8 man days of work and yields a profit of...

A farmer pays $0.20 for seed that he uses to grow wheat which he sells to...

A farmer pays $0.20 for seed that he uses to grow wheat which he sells to the miller for $0.40; the miller makes wheat flour and sells it to the baker for $0.60. The baker makes bread and sells it to the grocery store for $0.80 and the store sells it to the consumer for $1.00. The total contribution to the Gross Domestic Product (GDP) from all these transactions is A. $3.00 B. $2.00 C. $1.00 D. $0.20 2- ...

(a) Farmer Sherry can grow wheat and barley. She can grow 75 bushels of wheat or...

(a) Farmer Sherry can grow wheat and barley. She can grow 75 bushels of wheat or 125 bushels of barley on a hectare of her land for the same cost. The price of wheat is $2 per bushel and the price of barley is $0.80 per kilogram. Show the benefits to Sherry of specialization. What should she specialize in? Why ? (2) (b) You work at your school, making $15 per hour. Yesterday, you decided to cancel your two- hour...

(a) Farmer Sherry can grow wheat and barley. She can grow 75 bushels of wheat or...

(a) Farmer Sherry can grow wheat and barley. She can grow 75 bushels of wheat or 125 bushels of barley on a hectare of her land for the same cost. The price of wheat is $2 per bushel and the price of barley is $0.80 per kilogram. Show the benefits to Sherry of specialization. What should she specialize in? Why ? (2) (b) You work as a teacher at your school, making $15 per hour. Yesterday, you decided to cancel...

A farmer is interested in finding a new strain of alfalfa to grow on his land....

A farmer is interested in finding a new strain of alfalfa to grow on his land. He finds six new varieties and divides his land into thirty equally sized plots, with five randomly chosen plots for each strain. Strain Yield A 1849 A 1430 A 2389 A 1920 A 2145 B 1943 B 2354 B 1990 B 2063 B 2390 C 1791 C 2125 C 1084 C 1620 C 2033 D 2179 D 1846 D 1938 D 1410 D 1983...

Suppose a farmer in Georgia begins to grow peaches. He uses $1,000,000 in savings to purchase...

Suppose a farmer in Georgia begins to grow peaches. He uses $1,000,000 in savings to purchase land, he rents equipment for $80 comma 000 a year, and he pays workers $140 comma 000 in wages. In return, he produces 100 comma 000 baskets of peaches per year, which sell for $3.00 each. Suppose the interest rate on savings is 2 percent and that the farmer could otherwise have earned $45 comma 000 as a shoe salesman. What is the farmer's...

A farmer uses a greenhouse to grow his fruits and vegetables year round. He recently purchased...

A farmer uses a greenhouse to grow his fruits and vegetables year round. He recently purchased a machine that uses artificial intelligence to adjust the lighting to optimize plant growth. He wants to cut down on his energy costs so he started experimenting with two different light bulbs (HID & LED). The farmer would note down the daily kW usage when either is installed that day, each independent of the other. He randomly selected usage data and created the table...

Jayden is a mushroom farmer. He invests all his spare cash in additional mushrooms which grow...

Jayden is a mushroom farmer. He invests all his spare cash in additional mushrooms which grow on otherwise useless land behind his barn. The mushrooms double in weight during the first year, after which they are harvested and sold at a constant price per pound. Jayden's friend Isabella asks Jayden for a loan of $200, which she promises to repay after one year. (a) If the land is useless except for growing mushrooms, what is the opportunity cost of using...

Subjects