Question

MC Qu.60 The operations manager for the Blue Moon Brewing... The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). Two of his resources are constrained: production time, which is limited to 8 hours (480 minutes) per day, and malt extract (one of his ingredients), of which he can get only 675 gallons each day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract, while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg, and profits for Dark beer are $2.00 per keg. What is the time constraint?

Answer 1

Assume, number of lite beer keg as 'x' and the number of Dark beer keg as 'y'

Given that,

For one keg of lite beer, 2 minutes are required.

Hence, 'x' keg 2x minutes are required and for 'y' keg of Dark beer 4y minutes are required.

Total available time = 8 hours = 480 minutes.

Total time used for producing both types of beer: 2x + 4y
this must be less than total available time

So, time constraints:

2x + 4y ≤ 480

And for malt constraint:
5x + 3y ≤ 675

In order to maximize profit, the objective function: max 3x + 2y
solve:

2x + 4y ≤ 480 (time constraint)
5x + 3y ≤ 675 (malt constraint)

Solving: x = 90 keg of Lite beer
y = 75 keg of Dark beer

Profit = 420 per day