I want to solve the below question in Lingo software A soup company wants to det

Question

I want to solve the below question in Lingo software

A soup company wants to determine the optimal ingredients for its vegetable soup. The main ingredients are

Vegetables: Potatoes, Carrots, Onions, Meat, Water, Flavorings

The soup must meet these specifications:

a. No more than half of the soup can be vegetables

b. The ratio of water to meat should be 8:1

c. The amount of meat should be between 5 and 6 percent of the soup.

d. The flavorings should weight no more than 0.5 ounce.

The cost per ounce of the ingredients is $.02 for the vegetables, $.05 for the meat, $.001 for the water, and $.05 for the flavorings.

Formulate an LP model that will determine the optimal amounts of the various ingredients to achieve 15-ounce cans of soup at minimum cost for your specific scenario in the following table.

Explanation / Answer

Solution

Intial step is have to Identify the decision variables

X1 = quantity of potatoes in ounces

X2 = quantity of carrots in ounces

X3 = quantity of onions in ounces

X4 = quantity of meat in ounces

X5 = quantity of water in ounces

X6 = quantity of flavouring in ounces

Now write the objective function

Minimize    .02x1+.02x2+.02x3+.05x4+.001x5+.05x6

And write constraints for each specification

a) No more than half of the soup can be vegetables

X1+x2+x3 .05(15 oz.) thus

   X1+x2+x3 7.5 ounces

b) The ratio of water to meat should be 8:1

X5/x4 = 8/1 Cross multiplying yields x5 = 8x4.

Then , subtracting 8x4 from both sides in order to have all variables on the left hand side yields

-8x4+x5 = 0

c) The amount of meat should be between 5 and 6 percent of the soup.

This requires two constraints

                       x4 .05(15) which is x4 .75 ounce

                      x4 .06(15) which is x4 .90 ounce

d) The flavorings should weight no more than 0.5 ounce.

X6 .5 ounce

There is one additional constraint . The ingredients must add up to 15 ounces , the weight of a can of soup. Thus

X1+x2+x3+x4+x5+x6 = 15 ounces

Finally there are the non negativity constraints

All variables 0

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