A commercial truck dealership gets an allocation for 100 trucks from the manufacturer. Model A can be sold at $4500 above factory invoice, Model B at $5200, Model C at $4500, Model D at $4000. The dealership sold plenty of trucks last year, and is now including the halo model, (Model Elite-t Limited) in that allocation. This new model can be marked up at $16500 above invoice.

• At least 25% of the total order must be the fuel-efficient Model D
• Model C is a gigantic Truck and it can't count no more than 5% of the total order
• the dealer has to order at least one Model Elite-t Limited
• The dealership will get one Model Elite-t Limited for every 19 Model D ordered
• Since Model D and Model B share many common parts, the manufacturer produces plenty of them. So, they must account for 2/3 of the order.

The Mathematical Model I came up with is:

X₁ - Model A

X₂ - Model B

X₃ - Model C

X₄ - Model D

X₅ - Model E

X₆ - TOTAL

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X₄ <= .25* X₆

X₃ <= .05* X₆

X₅ = 19* X₄

X₆ <= (X₂ + X₄)*(2/3)

X₁ + X₂ + X₃ + X₄ + X₅ = X₆