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The Digital Star Company makes two different models of computer tablets, which are assembled on two different assembly lines. Line 1 can assemble 38 units of the Star model and 46 units of the Prostar model per hour, and line 2 can assemble 190 units of the Star model and 46 units of the Prostar model per hour. The company needs to produce at least 342 units of the Star model and 230 units of the Prostar model to fill an order. If it costs $300 per hour to run line 1 and $700 per hour to run line 2, how many hours should each line be run to fill the order at the minimum cost? What is the minimum cost? Step 1 Let x = the hours for line 1 and y = the hours for line 2. It costs $300 per hour to run line 1 and $700 per hour to run line 2. Thus, the cost function that we want to minimize is given by g = y. Line 1 can assemble 38 units of the Star model while line 2 can assemble 190 units of the Star model per hour. Since at least 342 units of the Star model need to be produced, the first constraint is given by X + Line 1 can assemble 46 units of the Prostar model while line 2 can also assemble 46 units of the Prostar model per hour. Since at least 230 units of the Prostar model need to be produced, the first constraint is given by ]y ? x +

The Digital Star Company makes two different models of computer tablets, which are assembled on two different assembly lines. Line 1 can assemble 38 units of the Star model and 46 units of the Prostar model per hour, and line 2 can assemble 190 units of the Star model and 46 units of the Prostar model per hour. The company needs to produce at least 342 units of the Star model and 230 units of the Prostar model to fill an order. If it costs $300 per hour to run line 1 and $700 per hour to run line 2, how many hours should each line be run to fill the order at the minimum cost? What is the minimum cost? Step 1 Let x = the hours for line 1 and y = the hours for line 2. It costs $300 per hour to run line 1 and $700 per hour to run line 2. Thus, the cost function that we want to minimize is given by g = y. Line 1 can assemble 38 units of the Star model while line 2 can assemble 190 units of the Star model per hour. Since at least 342 units of the Star model need to be produced, the first constraint is given by X + Line 1 can assemble 46 units of the Prostar model while line 2 can also assemble 46 units of the Prostar model per hour. Since at least 230 units of the Prostar model need to be produced, the first constraint is given by ]y ? x +

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The Digital Star Company makes two different models of computer tablets, which are assembled on two different assembly lines. Line 1 can assemble 38 units of the Star model and 46 units of the Prostar model per hour, and line 2 can assemble 190 units of the Star model and 46 units of the Prostar model per hour. The company needs to produce at least 342 units of the Star model and 230 units of the Prostar model to fill an order. If it costs $300 per hour to run line 1 and $700 per hour to run line 2, how many hours should each line be run to fill the order at the minimum cost? What is the minimum cost? Step 1 Let x = the hours for line 1 and y = the hours for line 2. It costs $300 per hour to run line 1 and $700 per hour to run line 2. Thus, the cost function that we want to minimize is given by g = X + y. Line 1 can assemble 38 units of the Star model while line 2 can assemble 190 units of the Star model per hour. Since at least 342 units of the Star model need to be produced, the first constraint is given by x + y? v Line 1 can assemble 46 units of the Prostar model while line 2 can also assemble 46 units of the Prostar model per hour. Since at least 230 units of the Prostar model need to be produced, the first constraint is given by X + y ? v
Transcribed Image Text:The Digital Star Company makes two different models of computer tablets, which are assembled on two different assembly lines. Line 1 can assemble 38 units of the Star model and 46 units of the Prostar model per hour, and line 2 can assemble 190 units of the Star model and 46 units of the Prostar model per hour. The company needs to produce at least 342 units of the Star model and 230 units of the Prostar model to fill an order. If it costs $300 per hour to run line 1 and $700 per hour to run line 2, how many hours should each line be run to fill the order at the minimum cost? What is the minimum cost? Step 1 Let x = the hours for line 1 and y = the hours for line 2. It costs $300 per hour to run line 1 and $700 per hour to run line 2. Thus, the cost function that we want to minimize is given by g = X + y. Line 1 can assemble 38 units of the Star model while line 2 can assemble 190 units of the Star model per hour. Since at least 342 units of the Star model need to be produced, the first constraint is given by x + y? v Line 1 can assemble 46 units of the Prostar model while line 2 can also assemble 46 units of the Prostar model per hour. Since at least 230 units of the Prostar model need to be produced, the first constraint is given by X + y ? v
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