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Questions 9 and 10 refer to the following: Creative Coffees sells 2 types of coffees to retail stores: regular and decaf. For the current month the company has 200 tons of coffee beans in inventory and has scheduled up to 300 hours of processing time for roasting. Each ton a regular coffee requires 1 ton of beans and 1 hour of roasting, and yields a net profit of $3000. Each ton of decaf also requires 1 ton of beans but needs 2 hours of roasting, and yields a net profit of $5000. To maximíze the net profit for the month, the manager of the production department has formulated the following linear program in which x is the number of tons of regular coffee and y is the number of tons of decaf coffee to produce: 3000x + 5000y x + x + Maximize y s 200 (bean constraint) 2y s 300 (time constraint) y 2 0 Subject to X. The feasible region corresponding to this linear program has four extreme points: (x = 0, y = 0), (x = 200, y = 0), (x = 100, y = 100), and (x = 0, y = 150). What is the optimal profit for Creative Coffees? Enter your answer rounded to the nearest dollar. %3D QUESTION 10 Refer to the prior question. True or false? If Creative Coffees could obtain either more beans or more processing time, then they could grow profits. C True C False

Questions 9 and 10 refer to the following: Creative Coffees sells 2 types of coffees to retail stores: regular and decaf. For the current month the company has 200 tons of coffee beans in inventory and has scheduled up to 300 hours of processing time for roasting. Each ton a regular coffee requires 1 ton of beans and 1 hour of roasting, and yields a net profit of $3000. Each ton of decaf also requires 1 ton of beans but needs 2 hours of roasting, and yields a net profit of $5000. To maximíze the net profit for the month, the manager of the production department has formulated the following linear program in which x is the number of tons of regular coffee and y is the number of tons of decaf coffee to produce: 3000x + 5000y x + x + Maximize y s 200 (bean constraint) 2y s 300 (time constraint) y 2 0 Subject to X. The feasible region corresponding to this linear program has four extreme points: (x = 0, y = 0), (x = 200, y = 0), (x = 100, y = 100), and (x = 0, y = 150). What is the optimal profit for Creative Coffees? Enter your answer rounded to the nearest dollar. %3D QUESTION 10 Refer to the prior question. True or false? If Creative Coffees could obtain either more beans or more processing time, then they could grow profits. C True C False

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Questions 9 and 10 refer to the following: Creative Coffees sells 2 types of coffees to retail stores: regular and decaf. For the current month the company has 200 tons of coffee beans in inventory and has scheduled up to 300 hours of processing time for roasting. Each ton a regular coffee requires 1 ton of beans and 1 hour of roasting, and yields a net profit of $3000. Each ton of decaf also requires 1 ton of beans but needs 2 hours of roasting, and yields a net profit of $5000. To maximize the net profit for the month, the manager of the production department has formulated the following linear program in which x is the number of tons of regular coffee and y is the number of tons of decaf coffee to produce: 3000x + 5000y x + x + Maximize y s 200 (bean constraint) 2y s 300 (time constraint) y 2 0 Subject to X, The feasible region corresponding to this linear program has four extreme points: (x = 0, y = 0), (x = 200, y = 0), (x = 100, y = 100), and (x = 0, y = 150). What is the optimal profit for Creative Coffees? Enter your answer rounded to the nearest dollar. %3D %3D QUESTION 10 Refer to the prior question. True or false? If Creative Coffees could obtain either more beans or more processing time, then they could grow profits. C True False
Transcribed Image Text:Questions 9 and 10 refer to the following: Creative Coffees sells 2 types of coffees to retail stores: regular and decaf. For the current month the company has 200 tons of coffee beans in inventory and has scheduled up to 300 hours of processing time for roasting. Each ton a regular coffee requires 1 ton of beans and 1 hour of roasting, and yields a net profit of $3000. Each ton of decaf also requires 1 ton of beans but needs 2 hours of roasting, and yields a net profit of $5000. To maximize the net profit for the month, the manager of the production department has formulated the following linear program in which x is the number of tons of regular coffee and y is the number of tons of decaf coffee to produce: 3000x + 5000y x + x + Maximize y s 200 (bean constraint) 2y s 300 (time constraint) y 2 0 Subject to X, The feasible region corresponding to this linear program has four extreme points: (x = 0, y = 0), (x = 200, y = 0), (x = 100, y = 100), and (x = 0, y = 150). What is the optimal profit for Creative Coffees? Enter your answer rounded to the nearest dollar. %3D %3D QUESTION 10 Refer to the prior question. True or false? If Creative Coffees could obtain either more beans or more processing time, then they could grow profits. C True False
Your city wants to determine how many postal substations are needed to service its population. The city has been divided into eight postal zones. Five possible locations for the substations have been identified. Each location can service a different number of zones, as indicated in the following table. Location Zones that can be served 1,2,3 12 1,4,5 3 2,4,5,8 3,5,6,7 4 5 6,7,8 In the text box, formulate a mathematical model to determine the fewest number of substations (and their locations) needed to service all 8 postal zones. Buy "formulate," you should define decision variables, the objective function, and all appropriate constraints. You need only supply the final mathematical model (you do not need to write out the objective function or constraints in words). You will not solve this. (Hint: define inappropriate variable for each location.)
Transcribed Image Text:Your city wants to determine how many postal substations are needed to service its population. The city has been divided into eight postal zones. Five possible locations for the substations have been identified. Each location can service a different number of zones, as indicated in the following table. Location Zones that can be served 1,2,3 12 1,4,5 3 2,4,5,8 3,5,6,7 4 5 6,7,8 In the text box, formulate a mathematical model to determine the fewest number of substations (and their locations) needed to service all 8 postal zones. Buy "formulate," you should define decision variables, the objective function, and all appropriate constraints. You need only supply the final mathematical model (you do not need to write out the objective function or constraints in words). You will not solve this. (Hint: define inappropriate variable for each location.)
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