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Algebra
Pregunta

A factory produces two kinds of health food \( A \...

A factory produces two kinds of health food \( A \) and \( B \) , busing ginseng and cordyceps. The compositions, per \( 100 g \) , of the two kinds of health food are shown below: 

There are \( 100 kg \) of ginseng and \( 15 kg \) of cordyceps available. Suppose the factory has to produce \( x \) hundred grams of health food \( A \) and \( y \) hundred grams of health food \( B \) . 

(a) Write down all the constraints on \( x \) and \( y \) . 

(b) Draw and shade the region that satisfies the constraints in (a) on a coordinate plane. 

(c) The profits from selling \( 100 \) g of health food \( A \) and \( 100 \) g of health food \( B \) are \( \$ 500 \) and \( \$ 400 \) respectively. How much health food \( A \) and health food \( B \) should be produced in order to maximize the profit? What is the maximum profit? (Assume all the health food can be sold.) 

Answer

Solución
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