Question

The Pittsburgh Cheese Company (PCC) has to decide the best production schedule for its cheese packages- Regular and Premium. The cheese packages (Regular and Premium) are made by blending mild cheddar cheese and sharp cheddar cheese. The cheese packages are sold in 1 lb packages. 1 lb package =16 oz.

Selling price and production cost of two types of cheese packages:

                                                Regular            Premium

Production(blending) Cost:       $0.20/pack                   $0.20/ pack

Selling Price:                            $1.95/pack                   $2.20/ pack

PCC buys cheese from Super Dairy. The Super Dairy quotes the following cost/ availability schedule.

                                                Mild                             Sharp

Availability:                             8100 lbs                       3000 lbs

Cost:                                       $1.20/lb                       $1.40/lb

The Regular brand: Each pack must contain at least 4 oz of sharp cheddar cheese.

The Premium brand: Each pack may contain at most 10 oz of mild cheddar cheese.

Decision Variables:

M1= lbs of mild to be bought for regular

M2= lbs of mild to be bought for premium

S1= lbs of sharp to be bought for regular

S2= lbs of sharp to be bought for premium

Formulate the problem as maximizing the profit.

Answer 1

M1= lbs of mild to be bought for regular
M2= lbs of mild to be bought for premium
S1= lbs of sharp to be bought for regular
S2= lbs of sharp to be bought for premium

Objective function: Maximize Z = total profit
Z = (1.95 - 0.20)(M1+S1) + (2.20 - 0.20)(M2+S2) - 1.20(M1+M2) - 1.40(S1+S2)
or,

Subject to,

Each pack(or lb.) of regular will contain at least 4 oz (0.25 lb.) of sharp. So, the % of sharp in regular should at least be 25%.
S1 >= 25%(M1 + S1)
or,

Each pack(or lb.) of premium will contain at most 10 oz (0.625 lb.) of mild. So, the % of mild in regular should at most be 62.5%.
M2 <= 62.5%(M2 + S2)
or,