A toy manufacturer wants to minimize her cost for producing two lines of toy airplanes. Because of the supply of materials, no more than 40 Flying Bats can be built each day, and no more than 60 Flying Falcons can be built each day. There are enough workers to build at least 70 toy airplanes each day. It costs $12 to manufacture a Flying Bat and $8 to build a Flying Falcon. What is the minimum possible cost each day?

Question

Stephanie

Mathematics

1 January, 17:42

A toy manufacturer wants to minimize her cost for producing two lines of toy airplanes. Because of the supply of materials, no more than 40 Flying Bats can be built each day, and no more than 60 Flying Falcons can be built each day. There are enough workers to build at least 70 toy airplanes each day. It costs $12 to manufacture a Flying Bat and $8 to build a Flying Falcon. What is the minimum possible cost each day?

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Madelynn Foster · Answer 1

Since Flying Falcon cost ($8) is cheaper than Flying Bat ($12), then the minimum possible cost each day would be the maximum possible Flying Falcon produced.

The maximum flying falcon produces is 60/day. Then, the amount of flying bat produced would be:

total = falcon + bat

70 = 60+bat

bat = 70-60 = 10

The minimum possible cost: falcon * falcon_cost + bat * bat_cost = 60*$8 + 10*$12 = $480+$120 = $600