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Posted: July 4th, 2021
1.) A manufacturer has a monthly fixed cost of $150,000 and a production cost of $50 for each unit produced. The product sells for $75 per unit. Find the break-even quantity.
2.) A manufacturer has a monthly fixed cost of $70,000 and a production cost of $17 for each unit produced. The product sells for $28 per unit. Find the break-even revenue.
3.) A manufacturer has a monthly fixed cost of $100,000 and a production cost of $20 for each unit produced. The product sells for $31 per unit. Find the break-even point.
4.) A company produces two types of bicycles; mountain bikes and racing bikes. It takes 9 hours of assembly time and 3⁄2 hours of mechanical tuning time to produce a mountain bike. It takes 4 hours of assembly time and 5 hours of mechanical tuning time to produce a racing bike. The company has at most 22 hours of mechanical tuning labor per week and at most 186 hours of assembly labor per week. The company’s profit is $70 for each mountain bike produced and $150 for each racing bike produced. The company wants to make as much money as possible. Let x = the number of mountain bikes they produce, and let y = the number of racing bikes they produce. Which of the following is the objective function for the problem?
5.) A company produces two types of nutritional supplements; Energize and Excel. Energize contains 24 mg of vitamin A, 76 mg of vitamin C and 21 mg of an herbal supplement. Excel contains 65 mg of vitamin A, 59 mg of vitamin C and 9 mg of the herbal supplement. An athlete is told that he needs at least 471 mg of vitamin A, 1115 mg of vitamin C and 429 mg of the herbal supplement for optimal athletic performance. The athlete wants to take the supplements, but at the lowest possible cost. Energize pills cost 40 cents each, while Excel pills cost 120 cents each. Let x = the number of Energize pills to take, and let y = the number of Excel pills to take. What are the constraints for this problem?
6.) A company produces two types of jackets; windbreakers and rainbreakers. The company has at most 63 hours of finishing time per week and 68 hours of packaging time per week. Each windbreaker jacket takes 47 minutes of finishing time and 28 minutes of packaging time per week, whereas each rainbreaker jacket takes 66 minutes of finishing time and 39 minutes of packaging time per week. The company’s profit for each windbreaker and rainbreaker jacket is 21 and 45, respectively. Let x denote the number of windbreaker jackets they should produce and y denote the number of rainbreaker jackets they should produce. The company wants to maximize profit. Set up the Linear Programming Problem for this situation. Math homework help
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