All of the following are examples of a “fundamental unit of business” that could be used in creating a bottom-up market model except:

a. Total physicians adopting a device within a given period

b. Total sales within a given period

c. Number of facilities purchasing a piece of equipment in a given period.

d. Number of procedures performed with a technology in a given period

A consumer product company makes two types of dishwasher detergents: regular and concentrate. The company has two manufacturing facilities for making detergent products. The first facility has an operating cost of $ 122.5 an hour and can produce 300 ounces of regular detergent products per hour and 220 ounces of concentrate detergent per hour. The second facility has an hourly operating cost of $ 220.0 and produces 350 ounces of regular detergent and 450 ounces of concentrate detergent per hour. The company received wholesale orders totaling 4,500 ounces of regular detergent and 5,200 ounces of concentrate detergent.

 

a. Formulate and solve the LP model that minimizes costs given the constraints. How many hours should the company operate each facility in order to fulfill the orders and minimize the operating cost? (Round your answers to 2 decimal places.)

The number of hours the company should operate the first facility	3.53
The number of hours the company should operate the second facility	9.83
Minimum operating cost	$ 8,595.04

 

b. Identify each binding constraint and report the shadow price and the range of feasibility. (Round your answers to 2 decimal places.) 

 

Shadow Price

Range of Feasibility             From                       To

Regular detergent constraint	Binding	$ 0.12	4,044.44	7,090.91
Comprehensive detergent constraint	Binding	$ 0.40	3,300.00	5,785.71

c. If the hourly operating cost of the second facility is reduced to $ 200, how many hours should the company operate each facility? What is the minimum operating cost in this scenario? (Round your answers to 2 decimal places.)

 

The number of hours the company should operate the first facility	3.53
The number of hours the company should operate the second facility	9.83
Minimum operating cost	_________

 

A consumer product company makes two types of dishwasher detergents regular and concentrate. The company has two manufacturing facilities for making detergent products. The first facility has an operating cost of $ 122.5 an hour and can produce 300 ounces of regular detergent products per hour and 220 ounces of concentrate detergent per hour. The second facility has an hourly operating cost of $ 2200 and produces 350 ounces of regular detergent and 450 ounces of concentrate detergent per hour. The company received wholesale orders totaling 4,500 ounces of regular detergent and 5,200 ounces of concentrate detergent

 

a. Formulate and solve the LP model that minimizes costs given the constraints. How many hours should the compony operate each facility in order to fulfill the orders and minimize the operating cost? (Round your answers to 2 decimal places.)

 

 

b. Identify each binding constrain and report the shadow price and the range of feasibility. (Round your answers to decimal places.) 

 

Shadow Price

Range of Feasibility              From               To

Regular detergent constraint
Concentrate detergent constraint