The operations manager for the Blue Moon Brewing Co produces

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. For the production combination of 135 Lite and 0 Dark which resource is not fully used (has slack)?

Select one:

a. Time only

b. Malt Extract only

c. Both Time and Malt Extract

d. Neither Time or Malt Extract

e. 5L + 3D <=480

Solution

Lite ---> L --> number of Lite beers

Dark --> D --> number of Dark beers

Each Lite results in profit of 3
So, L lites ---> profit = 3L dollars
Similarly, D darks ---> profit = 2D dollars
Objective function : Profit = $3L + $2D

Each lite needs 2min
So, L lites requires 2L minutes
Each dark needs 4 min
So, D darks requires 4D minutes
Total time available = 8 hrs = 480 min
So, Time constraint : 2L + 4D <= 480

Each lite needs 5 gal of malt extract
So, L lites ---> 5L gallons of malt extract
Each dark needs 3 gal of malt extract
So, D darks ---> 3D gal of malt extract
Total malt extract available = 675 gal
So, Malt extract constraint : 5L + 3D <= 675

Now, we are given that L = 135 and D = 0

2L + 4D <= 480
2(135) + 4(0) <= 480
270 <= 480
So, time is not fully used

5L + 3D <= 675
5(135) + 4(0) <= 675
675 <= 675
So, as can be seen, malt extract is fully used

So, only slack variable is TIME

Option A ---> ANSWER