Linear Optimization R

Question

I am new to optimization so please bear with me. Here is my problem:

A, B, C, D and E are percentages (18%,2%,1%,78%,1%)

Maximize sum (A(x) + B(x) + C(x) +D(x) + E(x)) ie maximize x ( x<=499572)

such that

A(x) <= 20076
B(x) <= 8619
C(x) <= 145
D(x) <= 465527
E(x) <= 5205

How do I frame this problem in R?

I was using LPsolve package but I am ok with any suggestions.

Forget R, you just need a simple calculator. The optimal x is the smallest x in the range which violates one of the 5 constraints (or, 499572 if none of the constraints are violated). You don't really need linear programming with just 1 decision variable. This blog post shows how to use LPsolve in R. — John Coleman
– John Coleman, Commented Sep 20, 2018 at 11:25
It is your third constraint which is binding, leading to an optimal solution of x = 14500. — John Coleman
– John Coleman, Commented Sep 20, 2018 at 11:38

G. Grothendieck · Accepted Answer · 2018-09-20 13:13:54Z

4

We restate the problem, omitting positivity constraints on the single scalar variable x, as:

maximize 1 * x
such that
 0.18 * x <= 20076 
 0.02 * x <= 8619 
 0.01 * x <= 145 
 0.78 * x <= 465527 
 0.01 * x <= 5205

so as a linear program we have the following optimum value of x:

library(lpSolve)

constr.mat <- c(.18, .02, .01, .78, .01)
RHS <- c(20076, 8619, 145, 465527, 5205)
soln <- lp("max", 1, constr.mat, "<=", RHS)
soln$solution
## [1] 14500

Of course, as pointed out in the comments below the question this problem can be solved trivially without linear programming by taking the least upper bound of x:

min(RHS / constr.mat)
## [1] 14500

Note

If what you really meant was not the problem stated in the question but rather this 5 variable problem:

max 0.18 * x1 + 0.02 * x2 + 0.01 * x3 + 0.78 * x4 + 0.01 * x5
such that
 0.18 * x1 <= 20076 
 0.02 * x2 <= 8619 
 0.01 * x3 <= 145 
 0.78 * x4 <= 465527 
 0.01 * x5 <= 5205

then we have

soln2 <- lp("max", constr.mat, diag(constr.mat), "<=", RHS)
soln2$solution
## [1] 111533.3 430950.0  14500.0 596829.5 520500.0

Again this is trivial to compute without linear programming:

RHS / constr.mat
## [1] 111533.3 430950.0  14500.0 596829.5 520500.0

edited Sep 20, 2018 at 13:13

answered Sep 20, 2018 at 12:20

G. Grothendieck

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1 Comment

pankaj negi Over a year ago

this works..thank you so much... i understand some of it. I will get back if I have more doubts :)

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