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An environmentally conscious customer hires a contractor to re$-$build his garage cement floor at

minimum cost. The contractor is trained to use $3$ main types of recycled materials when building

with eco$-$friendly cement: ash, dust and slag. Each cubic foot of ash, dust and slag costs $$2,$$$3$ and

$$5$ respectively. In order to make eco$-$friendly cement, the amount of dust plus twice the amount

of slag used should be at least $50$ cubic feet for small jobs like this one. Moreover, the amount of

dust used should not exceed the combined amount of ash and slag used. What mixture of materials

should the contractor use to produce exactly $300$ cubic feet of eco$-$friendly cement for this job?