Question

In: Finance

A company blends nitrogen and phosphorous to produce two types of fertilizers. Fertilizer 1 must be...

A company blends nitrogen and phosphorous to produce two types of fertilizers. Fertilizer 1 must be at least 50% nitrogen and sells for $55 per pound. Fertilizer 2 must be at least 55% phosphorous and sells for $45 per pound. The company can purchase up to 9000 pounds of nitrogen at $20 per pound and up to 12,000 pounds of phosphorous at $12 per pound.

Assuming that all fertilizer produced can be sold, determine the optimal blending plan for the company. What is the maximum profit?

Solutions

Expert Solution

Nitrogen Phosphorous Price Cost Profit
Fertilizer 1 50% 50% 55 16 39
Fertilizer 2 45% 55% 45 15.6 29.4
Price (Per Pound) 20 12
Max Quantity 9000 12000
Let Quantity of Fert 1 x
Let Quantity of Fert 2 y
Therefore,
Maximize 39x+29.4y -eq (3)
s.t.
0.5x+0.45y <= 9000 -eq (1)
0.5x+ 0.55 y <= 12000 -eq (2)
From Above Equation: Nitrogen is the limiting variable
This means that eq(2) is redundant
Now maximizing eq(3) w.r.t. eq (1)
Slope of eq (1) -1.11111
Slope of eq (3) -1.32653
Since, Eq (3) is steeper than Eq (1), then we can say that profit will be maximized at y=0, i.e. by producing fertilizer 1 only.
Therefore,
x = 18000
y = 0
Profit = 702000

Related Solutions

A company blends two materials: A and B to produce two types of fertilizers. Fertilizer 1...
A company blends two materials: A and B to produce two types of fertilizers. Fertilizer 1 must be at least 50% of A and sells for $65 per kilo gram. Fertilizer 2 must be at least 70% of B and sells for $48 per kilogram. The price of martial A is $10 per 100 kilo grams and the price of martial B is $14 per 100 kilo grams if they purchased over 10,000 kilo gram the price will be reduced...
A company blends two materials: A and B to produce two types of fertilizers. Fertilizer 1...
A company blends two materials: A and B to produce two types of fertilizers. Fertilizer 1 must be at least 50% of A and sells for $65 per kilo gram. Fertilizer 2 must be at least 70% of B and sells for $48 per kilogram. The price of martial A is $10 per 100 kilo grams and the price of martial B is $14 per 100 kilo grams if they purchased over 10,000 kilo gram the price will be reduced...
Fertilizer: In an agricultural experiment, the effects of two fertilizers on the production of oranges were...
Fertilizer: In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Thirteen randomly selected plots of land were treated with fertilizer A, and 10 randomly selected plots were treated with fertilizer B. The number of pounds of harvested fruit was measured from each plot. Following are the results. Fertilizer A 523 464 483 460 491 403 484 448 457 437 516 417 420 Fertilizer B 362 414 408 398 382 368 393 437 387...
Fertilizer: In an agricultural experiment, the effects of two fertilizers on the production of oranges were...
Fertilizer: In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Thirteen randomly selected plots of land were treated with fertilizer A, and 10 randomly selected plots were treated with fertilizer B. The number of pounds of harvested fruit was measured from each plot. Following are the results. Fertilizer A 523 464 483 460 491 403 484 448 457 437 516 417 420 Fertilizer B 362 414 408 398 382 368 393 437 387...
Fertilizer: In an agricultural experiment, the effects of two fertilizers on the production of oranges were...
Fertilizer: In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Twelve randomly selected plots of land were treated with fertilizer A, and 7 randomly selected plots were treated with fertilizer B. The number of pounds of harvested fruit was measured from each plot. Following are the results. Fertilizer A 464 483 441 491 403 466 448 457 437 516 417 420 Fertilizer B 362 414 412 398 382 377 393 Send data to...
The Donald Fertilizer Company produces industrial chemical fertilizers. The projected manufacturing requirements (in thousands of gallons)...
The Donald Fertilizer Company produces industrial chemical fertilizers. The projected manufacturing requirements (in thousands of gallons) for the next four quarters are 80, 50, 80, and 130, respectively. A level workforce is desired, relying only on anticipation inventory as a supply option. Stockouts and backorders are to be avoided, as are overtime and undertime. a. Determine the quarterly production rate required to meet total demand for the year, and minimize the anticipation inventory that would be left over at the...
Helen Keplinger must choose the amount of two wine types she will produce. Each liter of...
Helen Keplinger must choose the amount of two wine types she will produce. Each liter of Red wine returns $7 profit, while each liter of White wine returns $2 profit. The labor hours and bottling time used for each type of wine are given in the table below. Resources available include 169 labor hours and 74.25 hours of bottling process time. Assume the Helen Keplinger has more than enough grapes available to supply any feasible production plan. Red White Labor...
(1) As a consequence of fertilizer runoff from heavy farming, nitrogen levels are increasing in local...
(1) As a consequence of fertilizer runoff from heavy farming, nitrogen levels are increasing in local bodies of water. Two towns have taken competing approaches to deal with the problem, and you’ve been hired as a consultant to test whether either town has outperformed the other. (The goal is low N levels.) Here are the data, in the form of x1000mg/m3 . What can you say? Town A average N conc 10.0 sample size 14 standard dev 2.075 Town B...
A company produces and sells 3 types of organic fertilizer. A pound of Brand 1 earns...
A company produces and sells 3 types of organic fertilizer. A pound of Brand 1 earns a profit of $3 per pound. Brand II earns a profit of $4 per pound, and Brand III earns a profit of $3 per pound. 1 pound of Brand I requires 3 pounds of raw material and takes 2 hours of labor to produce it. 1 pound of Brand II requires 4 pounds of raw material and takes 3 hours of labor to produce...
Resource allocation. A coffee manufacturer uses Colombian and Brazilian coffee beans to produce two? blends, robust...
Resource allocation. A coffee manufacturer uses Colombian and Brazilian coffee beans to produce two? blends, robust and mild. A pound of the robust blend requires 12 ounces of Colombian beans and 4 ounces of Brazilian beans. A pound of the mild blend requires 6 ounces of Colombian beans and 10 ounces of Brazilian beans. Coffee is shipped in 138pound burlap bags. The company has 65 bags of Colombian beans and 30 bags of Brazilian beans on hand. How many pounds...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT