Question

Deluxe coffee is to be mixed with regular coffee to make at least 47 pounds of a blended coffee. The mixture must contain at least 10 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

Given :

Deluxe coffee is to be mixed with regular coffee to make at least 47 pounds of a blended coffee. The mixture must contain at least 10 pounds of deluxe coffee.

Let number of pounds of deluxe coffee = x

Let number of pounds of regular cofee = y

• Deluxe coffee costs ​$6 per pound and regular coffee ​$5 per pound

Minimize cost, z = 6x + 5y

where

x + y 47

x 10 and

y 0

The point of interaction are ( 10 , 37 ) and (47 , 0)

where x = 10 and y = 37

so,

Minimize cost,z at (10,37)= 6x + 5y

= 6*10 + 5*37

= 60 + 185

= 245

Therefour 10 pound of deluxe cofee and 37 pound of regular cofee are should be used to minimize​ costs.