The daily production process at a soda bottling company produces regular orange-flavored (x1 ), regular lemon-flavored(x2), diet orange-flavored (x3 ), and diet lemon-flavored (x4)drinks. The company operates 18 hours (1,080 minutes) per day and uses two types of syrups with daily available inventories of 260 and 220 gallons for syrup types 1 and 2, respectively. The demand for the two orange-flavored drinks combined is no more than 250 bottles and the two lemon-flavored drinks have a combined daily demand of at least 300 bottles. The company wishes to choose the production level for each type of drink in order to maximize its total profit. production time (minutes) Syrup 1 (gallons) Syrup 2 (gallons) profit unit Regular orange drink 1.2 0.30 0.10 $1.20 regular lemon drink 1 0.25 0.25 $1.50 diet orange drink 1.4 0.25 0.20 $1.80 diet lemon drink 2 0.40 0.30 $2.00

The daily production process at a soda bottling company produces regular orange-flavored (x1 ), regular lemon-flavored(x2), diet orange-flavored (x3 ), and diet lemon-flavored (x4)drinks. The company operates 18 hours (1,080 minutes) per day and uses two types of syrups with daily available inventories of 260 and 220 gallons for syrup types 1 and 2, respectively. The demand for the two orange-flavored drinks combined is no more than 250 bottles and the two lemon-flavored drinks have a combined daily demand of at least 300 bottles. The company wishes to choose the production level for each type of drink in order to maximize its total profit. production time (minutes) Syrup 1 (gallons) Syrup 2 (gallons) profit unit Regular orange drink 1.2 0.30 0.10 $1.20 regular lemon drink 1 0.25 0.25 $1.50 diet orange drink 1.4 0.25 0.20 $1.80 diet lemon drink 2 0.40 0.30 $2.00

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 107P

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A plant has sufficient capacity to manufacture any combination of four different products (A, B, C, D). For each product, time is required to be invested in four different machines, which is expressed in hours per kilogram of product, as shown in the following table as shown in the following table: (attached image) Each machine has an availability of 60 hours per week. Products A, B, C and D can be sold at $9, $7, $6 and $5per kilo, respectively. Variable labor costs are $2 per hour for machines 1 and 2, and $3 per hour for machines 3 and 4. The material costs for each kilogram of product A are $4. The material costs for each kilogram of products B, C, D and D are $4 each kilogram of products B, C and D are $1. What needs to be done:Formulate a profit-maximizing PL model given the maximum demand per product shown in the table (there are 16 variables). Note: The picture is in spanish, but I mean... is pretty easy to understand

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	production time (minutes)	Syrup 1 (gallons)	Syrup 2 (gallons)	profit unit
Regular orange drink	1.2	0.30	0.10	$1.20
regular lemon drink	1	0.25	0.25	$1.50
diet orange drink	1.4	0.25	0.20	$1.80
diet lemon drink	2	0.40	0.30	$2.00