demand of 230 banquet attendees can be expected at a dinner plate price of $80.00 each. A demand of 370 banquet attendees can be expected at a dinner plate price of $45.00 each. Catering Service A has a fixed cost of $1,800 and a marginal cost of $30 for each plate. Catering Service B has a fixed cost of $2,500 and a marginal cost of $22 for each plate. Costs for both caterers include the food, drinks, plates, utensils, tablecloths, glasses, crew, and cleanup. Dinner plates will only be sold as an entire unit. To justify company resources and to ensure the event will benefit the charity, the CEO insists the tickets be sold for no less than $40. All profits will go toward a charity of the committee's choosing. Additional spontaneous donation to the charity will be accepted the night of the banquet. Studies estimate that 5% will give $5, 23% will give $20, 18% will give $50, 7% will give $100, and 2% will give $500. Determine the break-even quantities for each of the two possible catering services. Catering Service A will at least break even at a minimum of ____ banquet attendees and a maximum of _ banquet attendees. Catering Service B will at least break even at a minimum of banquet attendees and a maximum of _ banquet attendees.

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter12: Algebra Of Matrices

Section12.CR: Review Problem Set

Problem 37CR

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A demand of 230 banquet attendees can be expected at a dinner plate price of $80.00 each. A demand of 370 banquet attendees can be expected at a dinner plate price of $45.00 each.
Catering Service A has a fixed cost of $1,800 and a marginal cost of $30 for each plate.
Catering Service B has a fixed cost of $2,500 and a marginal cost of $22 for each plate.
Costs for both caterers include the food, drinks, plates, utensils, tablecloths, glasses, crew, and cleanup.
Dinner plates will only be sold as an entire unit. To justify company resources and to ensure the event will benefit the charity, the CEO insists the tickets be sold for no less than $40. All profits will go toward a charity of the committee's choosing.
Additional spontaneous donation to the charity will be accepted the night of the banquet. Studies estimate that 5% will give $5, 23% will give $20, 18% will give $50, 7% will give $100, and 2% will give $500.

Determine the break-even quantities for each of the two possible catering services.

Catering Service A will at least break even at a minimum of ________ banquet attendees and a maximum of _______ banquet attendees.

Catering Service B will at least break even at a minimum of ________ banquet attendees and a maximum of _______ banquet attendees.

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