AboutPaul Klarreich Expertise All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions.
I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.
Experience I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.
Expert: Paul Klarreich Date: 6/17/2008 Subject: Maximum-minimum problems
Question After receiving $1000, you must carry out an intervention to increase the population of a marine mammal. You estimate that if M Gallons of medicine and N Gallons of nutrients are added to their marine habitat, then by next year this will save M^2+NM+12N lives. A Gallon of medicine costs $25 and a gallon of nutrients costs $5.
a) what is the cost of M gallons of medicine and N gallons of medicine?
b) To maximize within $ 1000, which combinations of medicine and nutrients would you put in the habitat?
C) which combination would you use? How many marine mammals would be saved by next year?
I tried to do it as an expression of M so I kept M as medicine but made N= 1000 - M
--- I got stuck on how to actually write these two into the problem
Answer Questioner: Maxime
Category: Calculus
Private: No
Subject: Maximization and Optimization
Question: After receiving $1000, you must carry out an intervention to increase the population of a marine mammal. You estimate that if M Gallons of medicine and N Gallons of nutrients are added to their marine habitat, then by next year this will save M^2+NM+12N lives. A Gallon of medicine costs $25 and a gallon of nutrients costs $5.
a) what is the cost of M gallons of medicine and N gallons of medicine?
b) To maximize within $ 1000, which combinations of medicine and nutrients would you put in the habitat?
C) which combination would you use? How many marine mammals would be saved by next year?
I tried to do it as an expression of M so I kept M as medicine but made N= 1000 - M
--- I got stuck on how to actually write these two into the problem
.....................................
Hi, Max, (OK to call you that?)
It looks as if your problem is:
Maximize S = M^2 + MN + 12N,
subject to the 'constraint':
Cost = 25M + 5N = 1000 [not M + N = 1000. I think that is a mistake.]
Solve that for N in terms of M, in order to eliminate N and get S = f(M).
