Author Question: A furniture store has set aside 800 square feet to display its sofas and chairs. Each sofa utilizes ... (Read 95 times)

Themember4 · **on:** Jun 24, 2018

A furniture store has set aside 800 square feet to display its sofas and chairs. Each sofa utilizes 50 sq. ft. and each chair utilizes 30 sq. ft. At least five sofas and at least five chairs are to be displayed.
a. Write a mathematical model representing the store's constraints.
b. Suppose the profit on sofas is 200 and on chairs is 100 . On a given day, the probability that a displayed sofa will be sold is .03 and that a displayed chair will be sold is .05 . Mathematically model each of the following objectives:1 . Maximize the total pieces of furniture displayed.2 . Maximize the total expected number of daily sales.3 . Maximize the total expected daily profit.

Question 2

Organizers of an Internet training session will charge participants 150 to attend. It costs 3000 to reserve the room, hire the instructor, bring in the equipment, and advertise. Assume it costs 25 per student for the organizers to provide the course materials.
a. How many students would have to attend for the company to break even?
b. If the trainers think, realistically, that 20 people will attend, then what price should be charged per person for the organization to break even?

sabina576 · **Reply #1 on:** Jun 24, 2018

Answer to Question 1

a. 50s + 30c 800
s 5
c 5
b. (1) Max s + c
(2) Max .03s + .05c
(3) Max 6s + 5c

Answer to Question 2

a. C(x) = 3000 + 25x
R(x) = 150x
Break-even students = 24
b. Cost = 3000 + 25(20)
Revenue = 20p
Break-even price = 175