Create an optimization variable named colors that is indexed by the primary additive color names and the primary subtractive color names. Include 'black' and 'white' as additive color names and 'black' as a subtractive color name.

colors = optimvar('colors',["black","white","red","green","blue"],["cyan","magenta","yellow","black"]);

Find the index numbers for the additive colors 'red' and 'black' and for the subtractive color 'black'.

[idxadd,idxsub] = findindex(colors,{'red','black'},{'black'})

idxadd = 1×2

     3     1

idxsub = 4

Create an optimization variable named colors that is indexed by the primary additive color names and the primary subtractive color names. Include 'black' and 'white' as additive color names and 'black' as a subtractive color name.

colors = optimvar('colors',["black","white","red","green","blue"],["cyan","magenta","yellow","black"]);

Find the linear index equivalents to the combinations ["white","black"], ["red","cyan"], ["green","magenta"], and ["blue","yellow"].

idx = findindex(colors,["white","red","green","blue"],["black","cyan","magenta","yellow"])

idx = 1×4

    17     3     9    15

Create and solve an optimization problem using named index variables. The problem is to maximize the profit-weighted flow of fruit to various airports, subject to constraints on the weighted flows.

rng(0) % For reproducibility
p = optimproblem('ObjectiveSense', 'maximize');
flow = optimvar('flow', ...
    {'apples', 'oranges', 'bananas', 'berries'}, {'NYC', 'BOS', 'LAX'}, ...
    'LowerBound',0,'Type','integer');
p.Objective = sum(sum(rand(4,3).*flow));
p.Constraints.NYC = rand(1,4)*flow(:,'NYC') <= 10;
p.Constraints.BOS = rand(1,4)*flow(:,'BOS') <= 12;
p.Constraints.LAX = rand(1,4)*flow(:,'LAX') <= 35;
sol = solve(p);

Solving problem using intlinprog.
LP:                Optimal objective value is -1027.472366.                                         

Heuristics:        Found 1 solution using ZI round.                                                 
                   Upper bound is -1027.233133.                                                     
                   Relative gap is 0.00%.                                                          


Optimal solution found.

Intlinprog stopped at the root node because the objective value is within a gap
tolerance of the optimal value, options.AbsoluteGapTolerance = 0 (the default
value). The intcon variables are integer within tolerance,
options.IntegerTolerance = 1e-05 (the default value).

Find the optimal flow of oranges and berries to New York and Los Angeles.

[idxFruit,idxAirports] = findindex(flow, {'oranges','berries'}, {'NYC', 'LAX'})

idxFruit = 1×2

     2     4

idxAirports = 1×2

     1     3

orangeBerries = sol.flow(idxFruit, idxAirports)

orangeBerries = 2×2

         0  980.0000
   70.0000         0

This display means that no oranges are going to NYC, 70 berries are going to NYC, 980 oranges are going to LAX, and no berries are going to LAX.

List the optimal flow of the following:

Fruit Airports

----- --------

Berries NYC

Apples BOS

Oranges LAX

idx = findindex(flow, {'berries', 'apples', 'oranges'}, {'NYC', 'BOS', 'LAX'})

idx = 1×3

     4     5    10

optimalFlow = sol.flow(idx)

optimalFlow = 1×3

   70.0000   28.0000  980.0000

This display means that 70 berries are going to NYC, 28 apples are going to BOS, and 980 oranges are going to LAX.

Create named index variables for a problem with various land types, potential crops, and plowing methods.

land = ["irr-good","irr-poor","dry-good","dry-poor"];
crops = ["wheat-lentil","wheat-corn","barley-chickpea","barley-lentil","wheat-onion","barley-onion"];
plow = ["tradition","mechanized"];
xcrop = optimvar('xcrop',land,crops,plow,'LowerBound',0);

Set the initial point to a zero array of the correct size.

x0.xcrop = zeros(size(xcrop));

Set the initial value to 3000 for the "wheat-onion" and "wheat-lentil" crops that are planted in any dry condition and are plowed traditionally.

[idxLand, idxCrop, idxPlough] = findindex(xcrop, ["dry-good","dry-poor"], ...
             ["wheat-onion","wheat-lentil"],"tradition");
x0.xcrop(idxLand,idxCrop,idxPlough) = 3000;

Set the initial values for the following three points.

Land      Crops           Method      Value
dry-good  wheat-corn      mechanized  2000
irr-poor  barley-onion    tradition   5000
irr-good  barley-chickpea mechanized  3500

idx = findindex(xcrop,...
    ["dry-good","irr-poor","irr-good"],...
    ["wheat-corn","barley-onion","barley-chickpea"],...
    ["mechanized","tradition","mechanized"]);
x0.xcrop(idx) = [2000,5000,3500];