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here is the task: One factory produces 3 types of cars: small, midsize and big. There are 6000 tons of steel and 60000 total time available. For each type of car produced, there must be 1000 cars of these types produced. Build an optimization model that maximizes profit. $$\begin{array}{l|ccc} & \text{Small} & \text{Midsize} & \text{Big} \\ \hline \text{Steel} & 1.5 & 3 & 5\\ \text{Work hours} & 30 & 25 & 40\\ \text{Profit} & 2000 & 3000 & 4000\end{array}$$

Here is what I got so far:

$X$: quantity of small type

$Y$: quantity of mid-size type

$Z$: quantity of big size type

Maximize: $2000X + 3000Y + 4000Z,\qquad X,Y,Z \ge 0$

Restriction: $$1.5X + 3Y + 5Z \le 6000$$ $$30X + 25Y + 40Z \le 60000$$

Where I'm stuck is how to write for each type of model produced, there must be at least $1000$ cars produced. I think it should be something like this but it feels incorrect: $$1.5X + 30X \ge 1000$$ $$3Y + 25Y \ge 1000$$ $$5Z + 40Z \ge 1000$$

Am I correct ?

Paul Sinclair
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James
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  • X, Y, and Z are the numbers of cars you are producing of each type. This means they are all restricted to be either 0 or at least 1000 – Connor James Feb 05 '16 at 21:20
  • As per Connor's comment, where you have $X, Y, Z \ge 0$, you should have $$X = 0 \text{ or } X \ge 1000\ Y = 0 \text{ or } Y \ge 1000\ Z = 0 \text{ or } Z \ge 1000$$ – Paul Sinclair Feb 06 '16 at 02:33

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