Question

Juiceco manufactures two products: premium orange juice and regular orange juice. Both
products are made by combining two types of oranges: grade 6 and grade 3. The oranges in
premium juice must have an average grade of at least 5, those in regular juice, at least 4.
During each of the next two months Juiceco can sell up to 1,000 gallons of premium juice and
up to 2,000 gallons of regular juice. Premium juice sells for $1,00 per gallon while regular
juice sells for 80 cents per gallon. At the beginning of month 1 Juiceco has 3,000 gallons of
grade 6 oranges and 2,000 gallons of grade 3 oranges. At the beginning of month 2, Juiceco
may purchase additional grade 3 oranges for 40 cents per gallon and additional grade 6
oranges for 60 cents per gallon. Juice spoils at the end of the month, so it makes no sense to
make extra juice during month 1 in the hopes of using it to meet month 2 demand. Oranges
left at the end of month 1 may be used to produce juice for month 2. At the end of month 1 a
holding cost of 5 cents is assessed against each gallon of leftover grade 3 oranges and 10 cents
against each gallon of leftover grade 6 oranges. In addition to the cost of the oranges it costs
10 cents to produce each gallon of (regular or premium) juice. Formulate an LP that could be
used to maximize the profit (revenues-costs) earned by Juiceco during the next two months.

Please formulate the LP problem and not provide coding.

Answer 1

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he o modef Max (IP-2p)+o.8x-1-23) 0.6PG t0-4* P3) (951.0 25 * G0.0) Pta-p+1-17+1-20): 61 761 3000 6-1 g6-P+g6-17+56 PGtS6 62t6-7 6-2 2000 73-IP+ST+S2 PztS3 2-2 6*96-1P +373-1P>=5*%-1P G6-17 t gx3 1 4x1 6*962p 3x93-2p 7= 5* 1_2p G6-2p+3x 93-2p 7: 4*1-2r K-1P = 100 -ITくニ 9_000 -2p く- 1000 _2yくニ9000 Global optimd coleion to objeatue Infeaorbrlfes total solwe terdions Valze 4466.66子 0.000000 Elapsed reutqu Seends O13

Model elass Total Vanicbles non lin ables O Integer vbles o tofal Censtainb non liner Censtn total non 3eoos 42 non inem non geros 0 Redzded Cost Valzee Vasiable IP 000 000 000000 600. O00 0 000000 1R 2000. 000 OO00000 X-2R 2000 O00 000000 0 000000 6 500000 P3 O00000 6. 350000 O00000o O O00000 S6 333 333 OO00000 G6- 3000 O00 G-IP G6-IR 233 333 O00000 1333 223 OO00000 GG-2 1333 333 O 000000 1333 333 0 00000 462R 43-1 0O00000 O100000 2000. 000 O000000 G3-1P 2000 000 O'00000D 43IR 000000 G3-2 Q00002 0 0000000 O 000000 G2-9p O000000 O'O0000D GS-De 000000 O 50000000ME-0

stack or Dual oice RDW Surplus 4466 66 1.600000 0, 000 O00 OP000000 3 6, 000 000 0 O00000 A 0. 000 0OD 0l00000 5. 0. b000000 o00o00 0 0000 00D O000000 O. 000000 O0000T 0, 0000000 O 5000DDO E-0 0000000 O5D0O00 -0 10. 2000 00 O 000000 0, 00000T O000000 12 2000 000 0 000 000 12 166666t E-0 4 O, o00000 O 9000000 15 O. 000000 6 t000000 16 000000 O q000 000 19 O 000 000 O-6333 333 Ac he Golzetion oe woiget 4466.66