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
A company invests $15,000.00 in an account that compounds interest annually. After two years, the account is worth $16,099.44. U
ANEK [815]
Principal = $15000
Amount = $16099.44
Rat of interest = r
Time = 2 years
Then
A = P(1 + r)^t
16099.44 = 15000 (1 + r)^2
(1 + r)^2 = 1.073
(1 + r)^2 = (1.036)^2
Then
1 + r = 1.036
r = 1.036 - 1
  = 0.036
  = 0.036/100
  = 3.6%
From the above deduction, it can be easily concluded that the correct option among all the options that are given in the question is the second option.
6 0
3 years ago
I need help please!:D
klasskru [66]

Answer:ion know

Step-by-step explanation:

5 0
2 years ago
Find the distance between A (2.6) and N (5,10). Round to the nearest tenth, if necessary.
Triss [41]

Answer:

5

Step-by-step explanation:

6 0
3 years ago
A panda and a giraffe start moving towards each other when they are 300 feet apart. The panda is running at a speed of P feet pe
liq [111]

Answer:

(2P + G) feet/min

Step-by-step explanation:

Speed of the panda = P

Speed of the giraffe = P + G

Thus,

Speed of Panda + Speed of Giraffe = approaching time

= P + P + G

= <u>2P + G</u>

Thus, The panda and the giraffe are approaching each other at a rate

of <u>(2P + G) ft/min</u>

<u></u>

<em>Hope it helps :)</em>

6 0
3 years ago
A line is represented by y * (312)x + 2. A perpendicular line goes through (6,-1). What would be the slope intercept form for th
natulia [17]

Answer:

13

Step-by-step explanation:

not sure sry

8 0
3 years ago
Other questions:
  • Simplify <img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B49%2F4%7D%20" id="TexFormula1" title=" \sqrt{49/4} " alt=" \sqrt{49/4} "
    5·2 answers
  • During the summer, Allie works on her uncle's dairy farm. One of Allie's many chores is to load bales of hay onto a wagon and ha
    13·2 answers
  • What is 25%(percent) Of 42
    7·2 answers
  • What are the signs of the x- and y-coordinates of points within each of the four quadrants in the coordinate plane?
    8·2 answers
  • 6+2&lt;5−4 and put the answer in set notation
    8·1 answer
  • Plz hurry <br><br>evaluate the expression<br> a+b where a=8 and b=19
    12·1 answer
  • Please Help Me Thanks! NO LINKS
    8·1 answer
  • Find the median of the data set. 100, 4, 12, 6
    6·1 answer
  • Harriet is helping her brother paint an art project like the one shown below. They plan to paint only the lateral faces. One qua
    10·1 answer
  • Pls help. Multiply 8/5 × 15/32
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!