Deluxe coffee is to be mixed with regular coffee to make at least 5151 pounds of a blended coffee. The mixture must contain at least 99 pounds of deluxe coffee. Deluxe coffee costs $55 per pound and regular coffee $33 per pound. How many pounds of each kind of coffee should be used to minimize costs?

9 pounds of deluxe

42 pounds of regular

Step-by-step explanation:

given data

Deluxe coffee mix with regular coffee = 51

mix contains deluxe coffee = 9 pounds

Deluxe coffee costs $5

regular coffee costr = $3

solution

we consider here

deluxe coffee = x lbs

regular coffee = y lbs

and

x+ y ≥ 52

and mixture contains at least 9 pounds of deluxe coffee

so  x ≥ 9

and

cost equation will be

cost C = 5x + 3 y

deluxe costs more than regular

and here we want to use as possible as to minimize the cost

so least amount

x + y = 51

x  = 9

y = 51 - 9

y = 42

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.