Here's the first one . . .
1. Minimizing Construction Costs
The UNICO department store has decided to enclose an 800 ft² area
outside the building. One side will be formed by the external wall of the store;
two sides will be made of pine boards, and the fourth side will be galvanized steel fencing.
If the pine boards cost $6/ft and the steel fencing costs $3/running foot,
determine the dimensions of the enclosure that can be erected at minimum cost.
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y | | y
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The area will be 800 ft².
We have: . .
The cost will be: .
Hence, the total cost is: . .
Substitute  into : .
. . and that is the function we must minimize.
Go for it!