Question

5. There are two kinds of products (called DA and GA) produced in your company every day. Alsothere are two kinds of materials (denoted by A and B) in need One DA costs one unit of A, one unit of B: one GA costs one unit of A, two units of B. You get $3000 when you sell one DA and $5000 for one GA. The supply of the two materials every day is 12,22. a)What is the maximal profit $ b) How many DA and GA should be produced every day to obtain this maximal profit? Number of DA = Number of GA

Answer 1

• a) $56000
• b) DA = 2, GA = 10

Explanation:

Given

• DA = A + B ⇒ $3000
• GA = A + 2B ⇒ $5000
• Number of A = 12
• Number of B = 22

We can see from the equations that

• GA - DA = B ⇒ $2000 and
• A = $1000 and B = $2000 in terms of profit

So greater use of unit B brings greater profit. We don't want any unit is left over, so get this equation.

• A + B = 12
• A + 2B = 22

Is the equation set to indicate use of the units A and B

Solving we get

• A = 2 and
• B = 10

It this case all the units are used and profit is maximum

• 2*$3000 + 10*$5000 = $56000

• Number of DA = 2
• Number of GA = 10