Question

A car repair shop blends oil from two suppliers. Supplier I can supply at most 45 gal with 3.9% detergent. Supplier II can supply at most 67 gal with 3.3% detergent. How much can be ordered from each to get at most 100 gal of oil with maximum detergent?

Answer 1

Maximize 0.039x + 0.033y

Subject to 0 ≤ x ≤ 45

0 ≤ y ≤ 67

x + y ≤ 100

Explanation:

From the given information:

To maximize detergent from at most 100 gal of oil.

Assumptions:

Let assume that oil with 3.9% detergent is denoted by x; &

oil with 3.3% detergent is denoted by y

To maximize:

0.039x + 0.033y

As x can only supply at most 45 gal;

Then, 0 ≤ x ≤ 45 (since no negative supply is possible)

And, y can only supply at most 67 gal;

Then, 0 ≤ y ≤ 67 (since no negative supply is possible)

Now, if we take at most 100 gal, we have;

x + y ≤ 100

Therefore, the final solution is:

Maximize 0.039x + 0.033y

Subject to 0 ≤ x ≤ 45

0 ≤ y ≤ 67

x + y ≤ 100