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 purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a 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: Bean Blend Regular DeCaf 60% 40% 40% 60% Brazilian Natural Colombian Mild 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 bland. 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 CR - pounds of Colombian beans purchased to produce Regular CD - pounds of Colombian beans purchased to produce Decal 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

Answer 1

Answer: Page 1 * from the data- >> Romans food market uses the two leading - Products are we assumed Regular coffee as x and the Decaf coffee as y. = Now, we solve accordingly with all the costs and revenues. BN – Brazil Natural CM - Colombia Mild PC - production cost, Pack.cost — Packaging costs. -> Let assume Romans Regular coffee and - Romans Decaf coffee. So, Regular coffee = x . Decaf coffee =Y SP = $3.3 /Pound S.P=$4.5/pound Quantity = xpounds - Quantity = y pounds Etee

- page-2 the current market price of Brazilian Natural is = $0.45 pear pound the The current market price of colombian Mild is = $0.67 per pound. » Proportion Brazilian Natural 0.6 0.6 colombian Mild 0.4 Packing cost = $0.84/pound Pic = $1.08 /pound Pack. Cost = $ 0.25 pound. Given costs:- 1) For Regular for Decof (0.45)*(0.6)*(x) (067) x (0.6)x(V) (0.67)x(0.4)*(x) (0:45)*(04) *(Y) zost = X(0.45X0:6+ Cost = Y(0,6X0.67 +0.4 X0:45) - 0.67X0.4) Cost = 0.582 y cost = 0.5280 X

Page 3 Given: 2) Packing cost -0.84X and Pico 1:08 Y 3) pack. Cost = 0.25 X Pack.cost = 0.257 selling price selling price (Revenue) (Revenue) 53.3 = 4.5 Y .: S.P-C.P = profit > 3.3% -(0.25% +0.84% +0.5280x) +4.5 - (0.25Y+1.08 Y+0.582) -) - 3.3-1,6288 +4:54 -1.912 y = 1672x+ 2.5889 (maximise) = 1.672 (1100) +2.588 (525) - BR = 1100 pounds (0.6) = 660 Pounds CR = 1100 pounds (0.4) - 140 pounds BD - 525 pounds (Oh) = 210 pounds CD - 525 pounds (0.6) - 315 pounds, : value of optimal solution = $1839.2+ $ 1,358.7 = 3197.9 $ X- -