Question

The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. 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. The breweryâs goal is to maximize profits.

1. What is the time constraints?

Answer 1

Answer:

2L + 4D = 480   {L = Lite Bear, D = Dark Bear, 480 = minutes in 8 hours}

Explanation:

The function to be maximised :

Profit Function = Price x Quantity (of Lite & Dark Bears) = 3L + 2D ; where-

L = Lite Bear, D = Dark Bear

Constraint 1 [Time Constraint] :- 2L + 4D = 480 ; where-

L = Lite Bear, D = Dark Bear, 480 = minutes in 8 hours

2 = minutes required per unit Lite Bear, 4 = minutes required per unit Lite Bear, 480 = minutes in total 8 hours (8x60)     {∵1hr = 60mins}

Similarly, Constraint 2  [Malt Extract Constraint] :- 5L + 3D = 675