I need help formulating the constraints for this Linear Programming optimization

ID: 398517 • Letter: I

Question

I need help formulating the constraints for this Linear Programming optimization problem

A = Male Customers Under 25 years old

B = Male Customers age 25-45

C = Male customers over 40 years old

X = Female Customers Under 25 years old

Y = Female Customers age 25-45

Z = Female customers over 40 years old

Min 4.5A + 3.5B + 5C + 3.8X + 4.2Y + 5.4Z

(Cost)

The constraints are as follows:

1) Survey at least 4000 customers

2) Survey at least 2000 customers who are age 25 or younger

3) Survey at least 800 customers who are 40 years of age or older

4) Ensure that at least 40% of those surveyed customers are male

5) Ensure that at most 100 of those surveyed male customers ar eolder than 40

Formulation of constraints -

A+B+C+X+Y+Z >= 4000 --> Total number of customers

A+X >= 2000 --> 25 or younger

C+Z <= 800 --> 40 or older

A+B+C >= 0.4*(A+B+C+X+Y+Z) => 0.6A+0.6B+0.6C-0.2*(X+Y+Z) >= 0 --> 40% are male

C < = 100 --> Male customers older than 40

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