5. An open rectangular box with a square base is to contain 500 m³ . What is the minimum cost if the base is made of material costing $3 per square m, and the sides are made of material costing S2 per square m.

Q: A construction company needs to dig a hole and fill it with gravel. The company has two options. The…

A: Given that

Q: 5. A piece of wire is with a length of 4 m is cut into two pieces, and the resulting two pieces are…

A: Let the length of the wire cut=xAll sides of square are same side length=yPerimeter= 4 y…

Q: A piece of wire 40 cm long is to be cut into two pieces . One piece wil bent to form a circle, the…

A: The total length of the wire is 40 cm and one piece is to be formed into a circle and another one is…

Q: Suppose now that the government decides to increase the number of quotas available to 72 units, but…

A: The following graph represents government's decision to increase the number of quotas available to…

Q: A plant food is made from three chemicals, labeled I, II, and III. In each batch of the plant food,…

A: Consider the provided question, Let amount of chemical I = x kg amount of chemical II = y kg and,…

Q: A wire b m long is cut into two pieces. One piece is bent into an equilateral triangle and the other…

A: given

Q: What are the dimensions for the cheapest possible rectangular box with a volume of 396 cm3  if the…

A:

Q: Two cities A and B are 8 km and 12 km, respectively, north of a river which runs due east. City B…

A: Given,  Two cities A and B are 8 km and 12 km respectively , north of a river which runs due…

Q: Suppose that a company needs 1,800,000 items during a year and that preparation for each production…

A:

Q: 9. The management of a large store wishes to add a fenced-in rectangular storage yard of 20,000…

A:

Q: 2. Suppose an airline policy states that all baggage must be rectangle-shaped with the sum of the…

A: We first calculate the side of square box then calculate its volume. Using formula Volume of cube…

Q: Determine the minimum cost of a retailer of motorized bicycles whose cost function is C(q) = 4860/q+…

A: Here the given cost function is: C(q)=4860q+15q+750000

Q: 4.1- You are building five identical pens adjacent to each other with a total area of 1000 m², as…

A: Given, Five identical pens are given below.

Q: A retailer anticipates selling 4,000 units of its product at a uniform rate over the next year. Each…

A:

Q: 5. A farmer wants to fence an area of 9600 square feet in a rectangular field and then divide it in…

A:

Q: 3. If the sum of two numbers is C, find the minimum value of the sum of their squares.

A:

Q: A power line is needed to connect a power station on the shore of a river to an island 4 miles…

A: From the given data,  Minimum cost = 2,500,000z+1,500,000(4-x) Let z be right angle triangle with X…

Q: A worker is to construct an open rectangular box with a square base and a volume of 128 ft. If…

A:

Q: A box with a square base and an open-top is to be constructed. The base will be made of material…

A:

Q: 1. Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width,…

A: Given Data: Assume, The length of the box is: l The width of the box is: w The height of the box is:…

Q: Suppose a company has fixed costs of $57,600 and variable costs of 4 9 x + 222 dollars per unit,…

A:

Q: Suppose consumers will purchase q units of a product at a price of 300 +1 dollars per unit. What is…

A: Express the equation for the Revenue function R(x). R(x)=xp(x) Here, x is the number of units and…

Q: From a tract of land, a developer plans to fence a rectangular region and then divide it into two…

A: Given: Cost of fence on outside = $20 per foot Cost of middle fence = $8 per foot Area of each lot =…

Q: maximize The Saddle Mine costs $14,000/day to operate, and it vields 50 oz of gold and 3000 oz of…

A:

Q: A plant food is made from three chemicals, labeled I, II, and III. In each batch of the plant food,…

A: Given - A plant food is made from three chemicals , labeled I, II, III . In each batch of plant…

Q: Lone Depot and Homes are two competing home improvement stores. Each claims to provide customers…

A: To find: The dimensions for minimum cost and also find the minimum cost. Given information: The…

Q: 1. A farmer wants to fence in a field and divide it into four side by side, equal areas. If he wants…

A: From the given data And, xy=8000&f(x,y)=2x+5y is the parimeter to minimize.

Q: Mr. Shamir employs two part-time typists, Inna and Jim, for his typing needs. Inna charges $15 an…

A: To work out the least cost under the given conditions in the word problem

Q: 23. Find two numbers whose sum is 10 and the sum of their squares is a minimum.

A: Let the two numbers be  x and yx+y=10⇒y=10-xx2+y2=SS=x2+10-x2   =x2+x2-20x+100   =2x2-20x+100

Q: A person on a special diet requires at least 100 units of protein and at most 24 units of…

A:

Q: You want to build a 1000 square foot rectangular infinity pool. Three of the sides will have regular…

A: Let the size of pool, x×y=xy=1000 Let the sides of the pool be x, x, y  and also length of Infinity…

Q: 6. The sum of two numbers is k. Find the minimum value of the sum of their cubes.

A: Minimum value of the sum of their cubes is

Q: A homeowner wants to build, along her driveway, a garden surrounded by a fence.   If the garden is…

A: Let the length (in feet) of the garden along the driveway and perpendicular to driveway be x and y…

Q: 4. A 12-meter string is cut into two pieces so that x meters will be used to form a circle and the…

A:

Q: 13. A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then…

A:

Q: A wire b is cut into two pieces. One piece is bent into an equilateral triangle and the other is…

A:

Q: 9. A student wishes to maximize the amount of poster space for an art exhibit. The requirements are…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 19. If the farmer in Exercise 18 wants to enclose 150 square meters of land, what dimensions will…

A: The minimum of a function can be obtained at the point where the slope of the function is 0. The…

Q: 5. A construction company is to transport 144 tonnes of stones to stone sites X and The Company pays…

A:

Q: A wire 12 inches long is cut into two, one part is bent in the form of a circle, and the other into…

A:

Q: According to postal regulations, a carton is classified as oversized if the sum of its height and…

A: NOTE- I have solved the second question as we are allowed to solve only one question in one session.…

Q: A farmer wants to start raising cows, horses, goats, and sheep and desires to have a rectangular…

A: We have to find maximum possible area that each of the four pens will enclose.

Q: Question 12. A homeowner wants to fence in a garden along the side of her house so she will only…

A:

Q: 6. A soda company is designing a new can that is more cost efficient. The base of the can costs…

A:

Q: From a tract of land, a developer plans to fence a rectangular region and then divide it into two…

A:

Q: A chicken farmer can buy a special food mix A at 20c per Kg and special food mix B at 40c per Kg.…

A: Let the farmer should buy x kg of food mix A and y kg of food mix B in order to minimize daily food…

Q: A cylindrical chemical storage tank with a capacity of 950m’ is going to be constructed in a…

A: Given that a cylindrical chemical storage tank with a capacity of 950m3 is going to be constructed…

Q: 4. Find the dimensions of the least expensive rectangular box which is three times as long as it is…

A:

Q: Suppose that in the inventory problem, the storage cost depends on the maximum inventory size,…

A: