Operation Research Problem.....Need help

Question One (10Marks)Kingsway Tyre Limited Company manufactures two typesof tyres (Michelin Tyres and Apollo Tyres). Each Michelin tyre requires twiceas much labour time as does each Apollo Tyre. If all tyres are Apollo only, thecompany can produce a total of 500 tyres a day. The market limits daily salesof the Michelin and Apollo tyres to 150 and 200 tyres respectively. Assume thatthe profit per Michelin tyre is $8 and $5 per Apollo tyre. (i) Formulate theproblem as a linear programming model to maximize total net profit [2 Marks] (ii) Writethe dual from the primal model (i above) andgive its economic interpretation [3 Marks] (

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Originally Posted by pngina

Question One (10Marks)Kingsway Tyre Limited Company manufactures two typesof tyres (Michelin Tyres and Apollo Tyres). Each Michelin tyre requires twiceas much labour time as does each Apollo Tyre. If all tyres are Apollo only, thecompany can produce a total of 500 tyres a day. The market limits daily salesof the Michelin and Apollo tyres to 150 and 200 tyres respectively. Assume thatthe profit per Michelin tyre is $8 and $5 per Apollo tyre. (i) Formulate theproblem as a linear programming model to maximize total net profit [2 Marks] (ii) Writethe dual from the primal model (i above) andgive its economic interpretation [3 Marks] (

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What have you tried?

I have an idea of part (i),formulating the problem as a linear model

And what did you come up with?

Let x and y represent the number of Michelin and Apollo tyres to be produced respectively;

Maximize Z = 8X + 5Y

Subject to;
y=500 or 0x+y=500 (a)
x≥150 or x+0y≥150 (b)
y≥200 or 0x+y≥200 (c)
2x=y or 2x-y=0 (d)
that's all I have and am not sure if its correct