Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

A foundry is developing a long-range strategic plan for buying scrap metal for its operations. The foundrycan buy scrap metal in unlimited quantity from two sources: Atlanta and Birmingham, and it receives thescrap daily by railroad cars.The scrap is melted down, and lead and copper are extracted. Each railroad car from Atlanta yields 1 ton ofcopper and 1 ton of lead, and costs $10,000. Each railroad car from Birmingham yields 1 ton of copper and2 tons of lead, and costs $15,000. The foundry needs at least 4 tons of lead and at least 2.5 tons of copperper day for the foreseeable future.1. In order to minimize the long-range scrap metal cost, how many raiload cars of scrap should bepurchased per day from each source

Sagot :

raphealnwobi

Answer:

The answer is below

Explanation:

Let x represent the number of railroad cars of scrap purchased per day from Atlanta and let y represent the number of railroad cars of scrap purchased per day from Birmingham.

Since Atlanta yields 1 ton of copper and 1 ton of lead while Birmingham yields 1 ton of copper and 2 tons of lead.

The foundry needs at least 2.5 tons of copper per day. Hence:

x + y ≥ 2.5      (1)

The foundry needs at least 4 tons of lead per day. Hence:

x + 2y ≥ 4      (2)

Plotting equations 1 and 2 using geogebra online graphing tool, we get the points that is the solution to the problem as:

(0, 2.5), (4, 0), (1, 1.5)

Car from Atlanta cost $10000 while car from Birmingham costs $15000. Therefore the cost equation is:

Cost = 10000x + 15000y

We are to find the minimum cost:

At (0, 2.5): Cost = 10000(0) + 15000(2.5) = $37500

At (4, 0): Cost = 10000(4) + 15000(0) = $40000

At (1, 1.5): Cost = 10000(1) + 15000(1.5) = $32500

The minimum cost is at (1, 1.5).

View image raphealnwobi
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.