1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Stells [14]
3 years ago
6

Bullco blends silicon and nitrogen to produce two types of fertilizers. Fertilizer 1 must be at least 40% nitrogen and sells for

$70 per pound. Fertilizer 2 must be at least 70% silicon and sells for $40 per pound. Bullco can purchase up to 80 pounds of nitrogen at $15 per pound and up to 100 pounds of silicon at $10 per pound. Assuming all fertilizer products can be sold, formulate and solve an LP to help Bullco maximize profits.
Mathematics
1 answer:
leva [86]3 years ago
8 0

Answer:

Maximize

z = 70(Xs1 + Xn1 ) + 40(Xs2 + Xn2 ) - 10 (Xs1 + Xs2 ) - 15(Xn1 + Xn2 )  

Subject to the constraints  

Xs1 + Xs2 ≤ 100

Xn1 + Xn2 ≤ 80

Xn1 ≥ 0.4 ( Xs1 + Xn1 )

Xs2 ≥ 0.7 ( Xs2 + Xn2 )

All Variables ≥ 0

Step-by-step explanation:

Firstly lets consider Xs1 and Xs2 to be the number of pounds of silicon used in fertilizer1 and fertilizer2 respectively

Also let Xn1 and Xn2 be the number of pounds of nitrogen used in fertilizer1 and fertilizer2 respectively

We know that the objective is to maximize the profits of Bullco.

z = [(Selling price of fertilizer1) (Amount of silicon and nitrogen used to produce fertilizer1) + (Selling price of fertilizer2) (Amount of silicon and nitrogen used to produce fertilizer2) - (Cost of silicon) (Amount of silicon used to produce fertilizer I and 2) - (Cost of nitrogen) (Amount of nitrogen used to produce fertilizer I and 2)]

so

z = 70(Xs1 + Xn1 ) + 40(Xs2 + Xn2 ) - 10 (Xs1 + Xs2 ) - 15(Xn1 + Xn2 )  

Now

Constraint 1;  At most, 100 lb of silicon can be purchased

Amount of silicon used to produce fertilizer 1 and 2 ≤ 100

Xs1 + Xs2 ≤ 100

Constraint 2; At most, 80 lb of nitrogen can be purchased

Amount of nitrogen used to produce fertilizer 1 and 2 ≤ 80

Xn1 + Xn2 ≤ 80

Constraint 3; Fertilizer 1 must be at least 40% of nitrogen

Amount of nitrogen used to produce fertilizer 1 ≥ 40% (fertilizer 1)

Xn1 ≥ 0.4 ( Xs1 + Xn1 )

Constraint 4; Fertilizer 2 must be at least 70% of silicon

Amount of silicon used to produce fertilizer 2  ≥ 70% (fertilizer 2)

Xs2 ≥ 0.7 ( Xs2 + Xn2 )  

so the formulization of the given linear program is,  

Maximize

z = 70(Xs1 + Xn1 ) + 40(Xs2 + Xn2 ) - 10 (Xs1 + Xs2 ) - 15(Xn1 + Xn2 )  

Subject to the constraints  

Xs1 + Xs2 ≤ 100

Xn1 + Xn2 ≤ 80

Xn1 ≥ 0.4 ( Xs1 + Xn1 )

Xs2 ≥ 0.7 ( Xs2 + Xn2 )

All Variables ≥ 0

You might be interested in
Lee Jenkins worked the following hours as a manager for a local Pizza Hut: 82,61,7
emmainna [20.7K]

Answer:

223 hours

Step-by-step explanation:

Total hours worked by Lee = sum of all the hours worked

That’s

82 + 61 + 7 + 73 = 223 hours

Therefore, Lee worked 223 hours as manager for the local Pizza Hut

5 0
3 years ago
00013 in scientific notation
Svet_ta [14]
1.3 x 10^1

hope that helped
let me know if i am right please

7 0
3 years ago
What is 2/3 + 3/4 I don’t understand it at all
victus00 [196]

Answer:

6/12 or half

Step-by-step explanation:

this would be the answer because the lowest common denominator of 4 and 3 is 12 so you'd multiply them you'd get 12 then multiply 2 and 3 and get six therfore the answer is 6/12 or 1/2

6 0
3 years ago
Read 2 more answers
Amanda bought $500 bond with a 6% coupon that matures in 20 years. What are amanda's total annual earnings for this bond?
horrorfan [7]

Answer:

dont listen to this kid its $30.00 on APEX

Step-by-step explanation:

5 0
3 years ago
I skipt thought the lesson pls help
Karo-lina-s [1.5K]

Answer:

I'm not sure but the last one I think is wroght

4 0
3 years ago
Read 2 more answers
Other questions:
  • You use 4 gallons of water on 14 plants in your garden. At this rate, how much water will it take to water 35 plants?
    9·2 answers
  • Help me on number 7 pls
    12·2 answers
  • Mr. Chang bought 264 pencils to divide evenly among his 22 students. How many pencils did each student receive?
    9·2 answers
  • A Medical Terminology course has 150 total students. On the first exam 96 students passed. What is the percentage of students th
    10·2 answers
  • Nine years ago, Tarah opened a savings account with her bank. She started with a balance of $359 and has not made any withdrawal
    10·1 answer
  • Please help me on step 4
    9·1 answer
  • Which is the best approximation for the solution of the system of equations?
    14·1 answer
  • PLZ ANSWER BRAINLIEST
    11·2 answers
  • Fifty cupcakes cost 129. What is the unit price for one cupcake?​
    6·2 answers
  • Jon rides his bike 5 miles in 40 minutes Paul rides his bike 8 miles in 40 minutes if they continue at this rate how far will ea
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!