Question

Problem 4-13 (Algorithmic) Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store's leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a purchased from price 12% higher than the market price the distributor pays for the beans. The current market price is $0.45 per pound for Brazilian Natural and $0.67 per pound for Colombian Mild. The compositions of each coffee blend are as follows: Blend DeCaf Regular Bean 40% Brazilian Natural 60% 60% Colombian Mild 40% Romans sells the Regular blend for $3.3 per pound and the DeCaf blend for $4.5 per pound. Romans would like to place an order for the Brazilian and Colombian coffee beans that will enable the production of 1100 pounds of Romans Regular coffee and 525 pounds of Romans DeCaf coffee. The production cost is $0.84 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.08 per pound. Packaging costs for both products are $0.25 per pound. Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit. Let BR pounds of Brazilian beans purchased to produce Regular BD pounds of Brazilian beans purchased to produce DeCaf pounds of Colombian beans purchased to produce Regular CR pounds of Colombian beans purchased to produce DeCaf CD If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a plus sign before the blank. (Example: -300) The complete linear program is Max 660 X X + 210 X+ 440 315 s.t. 1X 1 X 1100 1 X 1 X= 525 0X 1.67X X 2.5 2.5 X 0X X -1.67 BR, BD, CR, CD 2 0 1O If required, round your answer to the nearest cent. 3089.65X Value of the optimal solution = $

Answer 1

Brosilran bean 100 Colombian bean o187, &0.67 -6 + C0-12)(06+) To tal 3-3 (BR tCR) 4s (BD HED) Cost of raw materi ab( bean)-0-50 ED) 01504) (CRICD) BR+ to504 CR+0-00 O SOY BRTO504BD (BR+CR)(1.08) (BDrco) production Calt 084 4 o25 (BR +CR)t (02s) (8D +cb) pactoging Packaging -preduction Total profit 3-3(BR+CR) 5 (EDICD)-0-So4( BRIBD)O0y (RCD) + u-5 -0-89(BRICR) -1-08) (BB4CD) - Co25)(BR+CR) co 25)( 80+CD)

3.3BR +3.3CR +4 5BD+45CD-0-504 BR-0.5DUBD-075D CR -07504 CD -O.4 BR -0-S4CR-102 BD -toSCD -0-25 BR 25CR -O25BD- 2.5 CD = 3.3BR-0.504 BR-0.84 BR-0.25BR + 3-3CR--1504 CR -084CR -0.25CR + 4.5 BD-O 504BD -1.08 BD -O.25 BD + 4.5CD -o7504CD -108 CD -0.25CD 1706 BR 14596 ER+26GG PBD +- +2.4196 CD Constoraih ane BR CR O4 BR-O G CR -6 O6 O.4 BD C.D 6 BD-O4CD 0 0.4 O G BR+ CR = 1100 BD+ CD 525 Complete linas Progrom i Max 1F06 BR Marn 1us96 CR +2.4196 CD + 2.666 BD + 1706 BR 11O0 1 ICR I BR 525 ICD I BD OGCR O.G BD Ou cD

oling eg 1BE o.4 BR -O6CR Ou BR to4cR uuo oM BR O.6CR I CR CP uuo Subatitute in ea BR BR 1100-4uO ) BR CO BD+CD = 525-6 O-6 BD-0.4CD O (4 get o.6 (8) eg Solving xO e O.68D 10.6 CD 315 &D+ CD= 525 6 BD- 0 4CD- 1 CD 3 IS in eg Substitut CD: 215 BD -525-31S 210 BDr 315525 . CR -440, BP 210,CD 315 BR- 660 optimal nolution is 1-0GBR 2.666 2D +1459 GR+2.4l 96 CD 1-706 6601 2 666 2101-u596 Uu 0t2.41961 315 - 3090 21 optimal xolut