The question is about GAMS programming language which is used in linear programming methods. So that, the…

Let a₂ units of Product A be sold in Sales Area 2

Let a₃ units of Product A be sold in Sales Area 3

Let a₄ units of Product A be sold in Sales Area 4

Let b₁ units of Product B be sold in Sales Area 1

Let b₂ units of Product B be sold in Sales Area 2

Let b₃ units of Product B be sold in Sales Area 3

Let b₄ units of Product B be sold in Sales Area 4

Let c₁ units of Product C be sold in Sales Area 1

Let c₂ units of Product C be sold in Sales Area 2

Let c₃ units of Product C be sold in Sales Area 3

Let c₄ units of Product C be sold in Sales Area 4

Let d₁ units of Product D be sold in Sales Area 1

Let d₂ units of Product D be sold in Sales Area 2

Let d₃ units of Product D be sold in Sales Area 3

Let d₄ units of Product D be sold in Sales Area 4

Let e₁ units of Product E be sold in Sales Area 1

Let e₂ units of Product E be sold in Sales Area 2

Let e₃ units of Product E be sold in Sales Area 3

Let e₄ units of Product E be sold in Sales Area 4

Our objective function is to maximize profit i.e.

Maximize Z = 4.8a₁ + 3.75a₂ + 4a₃ + 4.75b₁ + 5b₃ + 4.5b₄ + 3.75c₁ + 3.3c₂ +3.5c₄ + 5.25d₁ + 5d₂ +5.15d₃ + 5.05d₄ + 5.04e₂ + 5.25e₃ +5.15e₄

Now applying the time constraints:

1(a₁ + a₂ + a₃) + 1.25(b₁ + b₃ + b₄) + 0.75(c₁ + c₂ + c₄) +1.25(d₁ +d₂ + d₃ + d₄) + 1.2(e₂ + e₃ + e₄) <= 50000

Demand Constraints

Production of each product should be less than or equal to the sum of demand in all Sales Area.

a₁ + a₂ + a_{3 < =12000}

b₁ + b₃ + b_{4<= 6000}

c₁ + c₂ + c_{4 <= 17000}

d₁ +d₂ + d₃ + d_{4<= 15000}

e₂ + e₃ + e_{4 <=14000}

_{Supply for the product in each area should be less than or equal to the demand for that product in that area}

a_{1< =6000 ,} a_{2< =2000,} a₃ < = 4000

b₁ <= 3000,  b₃ <= 1000 ,  b₄ <= 2000

c₁ <=6000 c₂ < =6000, c₄ < =5000

d1<=5000,   d₂<=5000,   d₃<=3000,   d₄<=2000

e₂ <= 9000,  e₃< =2000,  e₄ <= 3000

Finally the time constraint,

The time required for production should be less than or equal to 50000

i.e. (Time required per unit production of product * Number of Units) for all products <= 50000

1(a1+a2+a3+a4) + 1.25(b1+b2+b3+b4) + 0.75(c1+c2+c3+c4) + 1.25(d1+d2+d3+d4) + 1.2(e1+e2+e3+e4) < =50000

Solved this problem using excel solver. Please check the image with answer. Let me know if you require the spreadsheet.

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