For each problem listed below:
Q1. (30 points) Problem 21(a) on page 34 of the course pack
(finished and unfinished tables and chairs). Just follow the instructions above;
do not bother with parts (b) and (c).
Q2. (30 points) Problem 23 on page 34 of the course pack
(products A, B, and C).
Q3. (40 points) You run a small dairy processing facility that buys raw milk from local farmers for $0.40 per gallon. This milk must be run through a pasteurizing machine at a further cost of $0.10 per gallon. The pasteurizing machine can process up to 15,000 gallons per day. Each gallon of raw milk run through the machine yields one gallon of whole milk, which can be sold for $0.65 per gallon.
Instead of selling whole milk directly, you can also run it through a separating machine at a cost of $0.20 per gallon. Each gallon of whole milk put through the separating machine yields one 0.8 gallons of skim milk and 0.2 gallons of cream. Skim milk and cream may be sold for $0.80 and $1.25 per gallon, respectively. The separating machine can process up to 10,000 gallons of whole milk per day.
You can also blend whole milk and skim milk to make lowfat milk, which sells for $ 0.85 per gallon. Each gallon of lowfat milk consists of 1/2 gallon of whole milk and 1/2 gallon of skim milk. You can blend up to 5,000 gallons of lowfat milk per day at a cost of $0.05 per gallon.
To meet commitments to your regular customers, you must sell at least 4,000 gallons of whole milk, 3,000 gallons of skim milk, and 2,500 gallons of lowfat milk. There is no such requirement for cream.
Each gallon of raw milk run through the pasteurizing machine uses 0.004 hours of labor, each gallon of whole milk run through the separating machine uses 0.01 hours of labor, and each gallon of lowfat milk blended uses 0.005 hours of labor. You have at most 150 hours of labor available.
Determine how to operate
the dairy so as to make the highest possible daily profit.