Chancellor Manufacturing makes two pumps for use in household reef aquariums. The Standard pump (Model A) requires 4.5 lbs of stainless steel while the Deluxe lightweight pump (Model B) 3.0 lbs of stainless steel. There are 63 lbs of stainless steel available during this production period. The combined production of both pumps must be at least 12 pumps. There are orders for at least 6 of the lightweight Model B. Lastly, management has decided that no more than 15 Model B pumps be produced.
Required:
a. Write the LP formulation which provides the optimal production schedule for the standard and deluxe pumps such that the cost is minimized.
b. Write the above LP formulation in Standard Form.
c. Using your grid page, graph the above LP formulation. Be sure to label axes, constraints, and the feasible region.
Answer:
The answer is below
Step-by-step explanation:
Chancellor Manufacturing makes two pumps for use in household reef aquariums. The Standard pump (Model A) requires 4.5 lbs of stainless steel while the Deluxe lightweight pump (Model B) 3.0 lbs of stainless steel. There are 63 lbs of stainless steel available during this production period. The combined production of both pumps must be at least 12 pumps. There are orders for at least 6 of the lightweight Model B. Lastly, management has decided that no more than 15 Model B pumps be produced.
The cost to produce one Standard pump is $150 and to produce one Deluxe pump is $210.
Solution:
a) Let x represent model pump A and let y represent model pump B.
Since There are 63 lbs of stainless steel available, hence:
4.5x + 3y ≤ 63
Both pumps must be at least 12 pumps. Therefore:
x + y ≤ 12
There are orders for at least 6 of the lightweight Model B:
y ≥ 6
Also, no more than 15 Model B pumps be produced:
y ≤ 15
The cost to produce one Standard pump is $150 and to produce one Deluxe pump is $210. The cost equation is:
Minimize Cost = 150x + 210y
b)
Hence the LP formation is:
Minimize Cost = 150x + 210y
4.5x + 3y ≤ 63
x + y ≤ 12
y ≥ 6
y ≤ 15
x ≥ 0.
c) The LP problem was solved using geogebra online graphing tool.
The points that satisfy the problem are:
(0, 6), (0,12), (6, 6)
At (0,6); cost = 150(0) + 210(6) = 1260
At (0,6); cost = 150(0) + 210(12) = 2520
At (6,6); cost = 150(6) + 210(6) = 2160
Hence the minimum cost is at (0, 6)
If the measures of two angles of a triangle are 96 and 17°, what is the measure of the third angle
A baseball has a diameter of 2.8 inches. How many baseballs will fit in a cylindrical barrel
that has a diameter of 4 ft and a height of 6 ft?
Answer:
5935 base balls
Step-by-step explanation:
Volume of a cylinder : pi * r² * h
r = Radius, h = height = 6ft
Diameter = 4ft ; Radius = diameter / 2 = 4/2 = 2ft
V = π * 2^2 * 6
V = 75.398223 ft³
Diameter of baseball = 2.8 inches
2.8 inches = 2.8 × 2.8 * 2.8 = 21.952 in³ = 0.0127037 ft³
Hence,
75.398223 ft³ / 0.0127037ft³
= 5935.1370
= 5935 base balls
Hey Can someone help me please
A person just purchased the vending machine shown. Each compartment has the dimensions of 5 inches by 7 inches by 17 inches. What is the volume of the compartment?
Answer: 595
Step-by-step explanation:
Find the y-intercept for the parabola defined by
this equation:
y=x^2 + 8x + 12
Separate the values with a comma.
Fred went to an arcade to play video games. He paid $2 for every 11 tokens he bought. He spent a total of $16 on tokens. Which equation can be used to determine t, the number of tokens Fred bought?
Answer:
D
Step-by-step explanation:
Since there are two types of values here: tokens and dollars, we will need to use the same value across numerators and denominators in the ratio.
Choice D has 11 tokens over $2 equals to t tokens over $16. In both fractions the numerator is tokens and denominator is dollars.
which graph represents the inequality x > 15
Answer:
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Solve the formula A=2πrh+2πr2 for h.
Answer:
h = (A - 2πr²)/(2πr)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
A = 2πrh + 2πr²
Step 2: Solve for h
[Subtraction Property of Equality] Subtract 2πr² on both sides: A - 2πr² = 2πrh[Division Property of Equality] Divide 2πr on both sides: (A - 2πr²)/(2πr) = hRewrite/Rearrange: h = (A - 2πr²)/(2πr)In a bag, there are ten identical balls, numbered 1 to 10. You let two persons, each pick one ball from the bag. Suppose the person who gets ball of 10 can get some reward, so each one prefers to get ball of 10. As we easily know, the probability of getting ball 10 for first person is 1/10. What is the probability of getting ball 10 for second person
Which graph is the answer
Answer:
Dis the answer
Step-by-step explanation:
5 + 8x < 6x + 12
8x - 6x < 12 - 5
2x < 7
x < 3.5
mark me as brainlistSolve for y. Thank you.
Answer:
[tex]y = \sqrt{ \frac{wz}{x} } [/tex]
hence c. Patrick Mahomes is right.
Malcolm buys a 5/6-pound bag of black beans and a 3/4-pound bag of pinto
Answer:
1 7/12Step-by-step explanation:
I think that you want to know how many total pounds of beans do you have.
Well, to find this, simply find the LCM of 6 and 4. That is 12.
So convert the fractions to have a denominator of 12.
10/12, 9/12
Now add:
(10+9)/12 = 19/12 = 1 7/12
Travis's income is $7200a month, and he plans to budget 1/2 of his income for rent and 1/6 of his income for electricity.What fraction of his income does he plan to spend each month on these two items together? Express your answer in lowest terms.
Answer:
Travis plans on spending 2/3 of his income which is $4800
Step-by-step explanation:
1/2 = 3/6 and 3/6 + 1/6 = 4/6 and 4/6 = 2/3
Answer:
2/3
Step-by-step explanation:
7200 / 2 = 3600 rent
7200/ 1/6 = 1200 electricity
3600 +1200 = 4800
4800/7200 = the same as simplified 48/72
We know our 12x table = 4/6
We can simplify 4/6 as 2/3
y=−2x+1
x−3y=11 find the solution using elimination.
Answer:
Step-by-step explanation:
Using first equation in the second gives you
x-3(-2x+1)=11
x+6x-3=11
7x-3=11
7x=14
x=2, making y=-2x+1 become
y=-2(2)+1
y=-4+1
y=-3 so the solution is the point
(2,-3)
Find the pattern and use it to list the next two terms in the sequence.
-3,6,-28,72,-360,2160, ___ ,___
Answer:
Step-by-step explanation:
a₁ = -3 = (-1)¹×3
a₂ = 6 = (-1)²×2×3
a₃ = -28 = (-1)³×2²×7
a₄ = 72 = (-1)⁴×2³×3²
a₅ = -360 = (-1)⁵×2³×3²×5
a₆ = 2160 = (-1)⁶×2⁴×3³×5
That's as far as I got. I can predict that a₇ is a multiple of -32 and a₈ is a multiple of 64, but I don't see the pattern with the other factors.
find the area of a square plot of side 12 cm
Answer:
area of a square
= side × side
= 12 × 12
=144cm^2
Oliver sets out 5 one-gallon buckets to collect rainwater. After a storm, of each bucket
is filled with water. Oliver wants to know how many total gallons of water he collects.
Which addition expression can you use to find how many
total gallons of water Oliver collects?
1. He collected 5 gallons of water.
2. We find this out by knowing 5 = 5.
Hope it helps! Good luck! :D
Whoever is awake I need help with math points and brainlest
Answer:
the first one or A. hope this helps.
Step-by-step explanation:
Identifica la base y el exponente; entonces halla el valor
53
Base
Exponente
Write the equation of the line of reflection in the following picture
Answer:
it is reflected in the x-axis so y=0
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE HELP ME WILL GIVE BRAILIST
Answer:
a) 24[tex]ft^2[/tex]
b) 52ft
Step-by-step explanation:
a)
This question asks to find the capacity of the container. This is essentially asking what the volume of the container is. This can be done by multiplying the length by the width by the height.
4 * 2 * 3
= 24
b)
This question is asking how much material was used to make the prism. This is essentially asking what the surface area of the prism is. This can be found by finding the area of all the sides of the prism and then adding it up. Since it is a rectangular prism, opposite faces are congruent, hence one only has to find the area of three faces, add it up, then multiply it by two to find the answer.
2 ( 4 * 2 ) + 2 ( 3 * 4 ) + 2 ( 2 * 3 )
= 2(8) + 2(12) + 2(6)
= 16 + 24 + 12
= 52
What percentage of 10000 is 1847?
the answer is,
541.42%
I think this is the answer.
Which of the following statements are not true about parallelograms?
Select all that apply.
1. The area of a parallelogram is half of the product of its length and width.
2. The angles formed by the diagonals of a parallelogram are complementary to each
other.
3. The diagonals of a parallelogram bisect each other.
4. A diagonal divides a parallelogram into two congruent triangles.
5. Two consecutive angles of a parallelogram are supplementary.
9514 1404 393
Answer:
1, 2
Step-by-step explanation:
1. The area of a parallelogram is the product of length and width. The given statement is FALSE.
2. The angles formed by the diagonals are linear pairs, so supplementary. The given statement is FALSE.
3. TRUE
4. TRUE
5. TRUE
__
Statements 1 and 2 are not true.
Express 13/3 as mixed fraction
Answer:
4*1/3
Step-by-step explanation:
easy we know for each 3/3 == 1
so:
3*4 == 12
1/3 is left over so,
4*1/3
Answer:
the answer is 4 1/3, i recommend using the app mathaway
12. The win-loss record for a football team is 15 wins and 9 losses. What percent of their games
did they win?
Answer:
62.5%
Step-by-step explanation:
if they won 15 and lost 9 games then they played a total of 24 games (15+9). Then you just divid the number of wins (15) by the total number of games they played (24). SO, 15/24=0.652 or 62.5%
Pleaaaaaase help this is due today
What does the statement “ The shortest distance between two points is the straight line between them” have to do with the Triangle Inequality Conjecture?
Do not answer this with one, none, or a ridiculous response please... this is serious
Answer:
https://geometryhelp.net/triangle-inequality-theorem/
Step-by-step explanation:
This is from that site. Visit it and you may find what you're looking for.
If we want to go from point A to point B, getting there through any intermediate point C, which is not on the straight line between A and B, is going to be longer. This should seem intuitively correct. But we will prove it formally.
Where do triangles come into this? Imagine that the line AB is a side of a triangle, ΔABC. Going from A to B is the straight, short way. Going there by first going to another point, C (which is the side AC) and then from C to B (which is the side CB) is going to be longer.
2x²+2 (2x) +5=0
solve indices
Step-by-step explanation:
2x²+4x+5=0
.....
solve it by using the factorisation method or completing the square method
don't mind the hand writing
am I correct btw
What is the answer for this?
What is the sum? 3x^2-2x-1/x-5+-2x^2+x-5/x-5
Answer: 5(1-x) over x
Step-by-step explanation: Combine the rational expressions using the least common denominator (LCD).