1. Your boss has entrusted you with managing the massive 400 Liter fish tank in the lobby of where you work; there are many sensitive and expensive fish in the tank, so you have to carefully manage the levels of certain minerals in the tank to keep them all alive and healthy. You need at least 10mg/mL of mineral A, at least 8 mg/mL of mineral B, and between 2.5 mg/mL and 5mg/mL of mineral C. There are two commercially made additives you can buy; Tropical Fish Friends is 50 dollars for a 100mL bottle, and it contains 4 grams of A, 2.5 grams of B, and 1 gram of C per bottle; Secret of the Sea is 40 dollars per 100 mL bottle, and it contains 3 grams of A, 3 grams of B, and 0.5 grams of C. (a) What are the linear inequalities of the constraints? Make two separate ones for C. (b) What is the objective function, the one we are trying to optimize? (c) What are the boundary points of the resulting constraint graph? What are the cost values at those points? Do I want the minimum value, or the maximum value? (d) The bottles are shelf stable for years, and you want to stock up on at least a year's worth. You have to treat the tank every 3 weeks, so many bottles of each should you buy at least?
1. Your boss has entrusted you with managing the massive 400 Liter fish tank in the lobby of where you work; there are many sensitive and expensive fish in the tank, so you have to carefully manage the levels of certain minerals in the tank to keep them all alive and healthy. You need at least 10mg/mL of mineral A, at least 8 mg/mL of mineral B, and between 2.5 mg/mL and 5mg/mL of mineral C. There are two commercially made additives you can buy; Tropical Fish Friends is 50 dollars for a 100mL bottle, and it contains 4 grams of A, 2.5 grams of B, and 1 gram of C per bottle; Secret of the Sea is 40 dollars per 100 mL bottle, and it contains 3 grams of A, 3 grams of B, and 0.5 grams of C. (a) What are the linear inequalities of the constraints? Make two separate ones for C. (b) What is the objective function, the one we are trying to optimize? (c) What are the boundary points of the resulting constraint graph? What are the cost values at those points? Do I want the minimum value, or the maximum value? (d) The bottles are shelf stable for years, and you want to stock up on at least a year's worth. You have to treat the tank every 3 weeks, so many bottles of each should you buy at least?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Your boss has entrusted you with managing the massive 400 Liter fish tank in the lobby of
where you work; there are many sensitive and expensive fish in the tank, so you have to
carefully manage the levels of certain minerals in the tank to keep them all alive and healthy.
You need at least 10mg/mL of mineral A, at least 8 mg/mL of mineral B, and between 2.5
mg/mL and 5mg/mL of mineral C.
There are two commercially made additives you can buy; Tropical Fish Friends is 50 dollars
for a 100mL bottle, and it contains 4 grams of A, 2.5 grams of B, and 1 gram of C per bottle;
Secret of the Sea is 40 dollars per 100 mL bottle, and it contains 3 grams of A, 3 grams of B,
and 0.5 grams of C.
(a) What are the linear inequalities of the constraints? Make two separate ones for C.
(b) What is the objective function, the one we are trying to optimize?
(c) What are the boundary points of the resulting constraint graph? What are the cost values
at those points? Do I want the minimum value, or the maximum value?
(d) The bottles are shelf stable for years, and you want to stock up on at least a year's worth.
You have to treat the tank every 3 weeks, so many bottles of each should you buy at least?
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