Minimizing Construction Costs The management of the UNICO department store has decided to enclose a 945 ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. If the pine board fencing costs $7/running foot and the steel fencing costs $4/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (Round your answers to one decimal place.)

Answers

Answer 1

Answer:

Answer:

Pine board side = 16.4 ft

Steel fencing side = 57.5 ft

Step-by-step explanation:

Let 'B' be the length of each side constructed of pine boards, and 'S' be the length of the side with the steel fencing, the area (A) and cost (C) functions are:

$945 = B*S\nB=(945)/(S) \nC= 4*S+7*2B\nC=4S+(13,230)/(S)$

The value of S for which the derivate of the cost function is zero, minimizes cost:

$C'=0=4+(-13,230)/(S^2)\n S=√(3,307.5) \nS=57.5 ft$

The value of B is:

$B=(945)/(57.5)\nB=16.4 \ ft$

Pine board side = 16.4 ft

Steel fencing side = 57.5 ft

Answer 2

Answer:

Final answer:

To minimize the construction costs for the enclosure, the dimensions should be calculated using the calculus optimization technique. By incorporating the cost and area requirements into calculated equations and solving, you will find x = 2 times y. This is how you minimize the cost.

Explanation:

This problem involves the application of calculus and optimization techniques. Given that the area of the enclosure needs to be 945 ft2, and that it is adjacent to an external wall of the department store, we can infer that its shape is rectangular.

Let the width of the enclosure parallel to the department store be x (feet), and its length perpendicular to the store be y (feet). According to the area requirement, we have the equation x*y = 945 ft2.

The cost of the enclosure is the sum of the cost of the pine board fences and the steel fence. Since 2 sides are made of pine boards, and 1 side made of steel, the cost can be expressed as C = 2xy p + y s, where 'p' is the cost of pine board per foot ($7), and 's' is the cost of steel per foot ($4).

Since we are looking for the minimum cost, we derive this equation and set it equal to zero to find the dimensions x and y. After substituting and simplifying, we find that the minimum cost is obtained when x = 2 y. By substituting this into the area equation, we can solve for the dimensions of the enclosure.

Learn more about Calculus Optimization here:

brainly.com/question/30795449

#SPJ3

Related Questions

Part EChristopher Columbus set sail from Spain in 1492. In what year did the Civil War end?
A resident of Bayport claims to the City Council that the proportion of Westside residents (1) with income below the poverty level is lower than the proportion of Eastside residents (2) The City Council decides to test this claim by collecting a random sample of resident incomes from the Westside of town and a random sample of resident incomes from the Eastside of town. Seventy-six out of 578 Westside residents had an income below the poverty level. Hundred-and-twelve out of 688 Eastside residents had an income below the poverty Specify the hypotheses. Calculate the value of the test statistic (round to 4 decimal places). Calculate the p-value (round to 4 decimal places).
Right triangle ABC is shown. Which of these is equal to cos(A)?A) cos(B) B) cos(C) C) sin(B) D) sin(C)
X÷79 + 72 - 18 hellppppp
Find the sum: 3 4/5+2 1/4 i need helpnplzzz

T he equation for a parabola with directrix y = –p and focus (0, p) is:1.What is the parabola’s line of symmetry?

y-axis
x-axis
x = p
x = -p

Answers

The equation for a parabola with directrix y = –p and focus (0, p)

The distance between vertex and directrix is P

Also the distance between vertex and focus is also P

Focus (0,p) so focus lies on y axis

Directrix line is paralled to focus point

So Directex crosses the x axis .

Hence line of symmetry lies is the y-axis.

The graph is attached below.

Please help as soon as you can :(Alicia rolls two fair number cubes numbered from 1 to 6. She first defines the sample space, as shown below:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5,) (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5,) (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5,) (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5,) (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5,) (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5,) (6, 6)
Based on the sample spaces, what is the probability of getting a total of 7?

A.) 4/36
B.) 5/36
C.) 6/36
D.) 8/36

Hope you can help!

Answers

The answer is C
hope this helped...

Answer:

6/36

(C.)

I hope this helps you if it hasn't already! Bye.

I Need help ASAP!!!

Answers

Answer:

x = 15, AOB = 15, BOC = 165

Step-by-step explanation:

Assume that this is a straight line

2x - 15 + 11x = 180

Combine like terms

13x - 15 = 180

Add 15 on both sides

13x = 195

Divide 13 on both sides

x = 15

Substitute x for 15 in both equations

2(15) - 15 = 15

11(15) = 165

(For checking purposes, 165 + 15 = 180)

PLEASE HELP!!!Amy, Dan, and Mike are competing in a cooking competition. They all used different amounts of milk from a container holding 6 gallons of milk.

Amy used 13% of the total milk in the container.
Dan used 0.14 of the total milk in the container.
Mike used 0.5 gallon of the total milk in the container.
Who used the greatest amount of milk from the container? Show your work and explain your answer in words.

Must use inverse operations

Answers

I'm not sure what your teacher means by "must use inverse operations".

Anyways, Amy uses 13% of the total milk (6 gallons). So she uses 0.13*6 = 0.78 gallons.

Then we're told that Dan used 0.14 of the total milk. So 0.14*6 = 0.84 to indicate Dan used more than Amy. Dan also used more than Mike because 0.84 gallons is larger than 0.5 gallons.

Answer: Dan used the most milk (0.84 gallons)

1. SPOTLIGHTS Ship A has coordinates (–1, –2) and Ship B has coordinates (–4, 1). Both ships have their spotlights fixated on the same lifeboat. The light beam from Ship A travels along the line y = 2x. The light beam from Ship B travels along the line y = x + 5. What are the coordinates of the lifeboat?

Answers

Answer:

( 5 , 10 )

Step-by-step explanation:

Solution:-

- There are two ships, A and B, currently located by their respective coordinates in the cartesian coordinate system:

Position of ship A: ( - 1 , -2 )

Position of ship B: ( -4 , 1 )

- Both ships try to locate a lifeboat. The spotlights used by each ship are modelled as straight line functions of cartesian coordinate originating from their respective ships.

- Spot lights for each ship were able to locate the same lifeboat. The respective spotlights are modelled by the following functions:

Spotlight Ship A: y = 2x

Spotlight Ship B: y = x + 5

- To locate the position of the lifeboat with respect to the origin ( 0 , 0 ) we will use the spotlight model functions and equate them. This is because the spotlights must converge or meet at the position of lifeboat provided the lifeboat is found by both ships.

- Therefore,

Spotlight A = Spotlight B

y = 2x = x + 5

2x = x + 5

x = 5 , y = 10

Answer:The two spotlight meet at the coordinates ( 5 , 10 ). This is also the position of the lifeboat located by both the ships.

You have a bowl with 5 orange, 6 blue, 3 green, 4 red and 7 yellow candies. What is the probability that choose an orange candy out of the bowl?