Question

Deluxe coffee is to be mixed with regular coffee to make at

least 43 pounds of a blended coffee. The mixture must
contain at least 12 pounds of deluxe coffee. Deluxe coffee
costs $6 per pound and regular coffee $5 per pound. How
many pounds of each kind of coffee should be used to
minimize costs?

Answer 1

We have to minimize the cost of 51 pounds of blended coffee.

The mixture must contain 13 pounds of deluxe coffee.

Deluxe coffee costs $4 per pound while regular coffee costs $3 for the same amount.

So, we need to maximize the concentration of regular coffee in the blended coffee to minimize our costs, but we must mix 13 pounds of deluxe coffee in order to make the blended coffee as it is the condition given to us in the problem.

Hence, apart from this 13 pounds, all the rest weight in blended coffee should come from the regular one.

Hence, the amount of regular coffee we have to use = (51 - 13) = 38 pounds.

Now, the cost of the 51 pounds of blended coffee

38×3+13×4 = ₹166.