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.
-What is the daily profit when producing the optimal amounts?
A)$0
B)$240
C)$420
D)$405
E)$505

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.
-What is the daily profit when producing the optimal amounts?
A)$0 
B)$240 
C)$420 
D)$405 
E)$505

Quizplus · Accepted Answer

To maximize profit, solve the linear programming problem: maximize 3L + 2D subject to 2L + 4D ≤ 480 (time constraint in minutes) and 5L + 3D ≤ 675 (malt extract constraint). Solving these inequalities, the optimal solution is L = 135 and D = 45, yielding a profit of 3(135) + 2(45) = $420.

The Operations Manager for the Blue Moon Brewing Co