Term Paper-Show the mathematical model for the total revenue (TR), which is the annual demand multiplied by the unit price

Term Paper-Show the mathematical model for the total revenue (TR), which is the annual demand multiplied by the unit price

4- A retail store in Des Moines, Iowa, receives shipments of a particular product from Kansas City and Minneapolis. Let x 5 units of product received from Kansas City y 5 units of product received from Minneapolis

a. Write an expression for the total units of product received by the retail store in Des Moines. b. Shipments from Kansas City cost $0.20 per unit, and shipments from Minneapolis cost $0.25 per unit. Develop an objective function representing the total cost of shipments to Des Moines.

c. Assuming the monthly demand at the retail store is 5000 units, develop a constraint that requires 5000 units to be shipped to Des Moines. 

d. No more than 4000 units can be shipped from Kansas City and no more than 3000 units can be shipped from Minneapolis in a month. Develop constraints to model this situation. 

e. Of course, negative amounts cannot be shipped. Combine the objective function and constraints developed to state a mathematical model for satisfying the demand at the Des Moines retail store at minimum cost.

5- For most products, higher prices result in a decreased demand, whereas lower prices result in an increased demand (economists refer to such products as normal goods). Let

d = 5 annual demand for a product in units.

p= 5 price per unit .

Assume that a firm accepts the following price–demand relationship as being a real- istic representation of its market:

d =5 800  –  10p

where p must be between $20 and $70.

a. How many units can the firm sell at the $20 per-unit price? At the $70 per-unit price? 

b. What happens to annual units demanded for the product if the firm increases the per- unit price from $26 to $27? From $42 to $43? From $68 to $69? What is the suggested relationship between per-unit price and annual demand for the product in units? 

c. Show the mathematical model for the total revenue (TR), which is the annual demand multiplied by the unit price.

d. Based on other considerations, the firm’s management will only consider price alternatives of $30, $40, and $50. Use your model from part (b) to determine the price alternative that will maximize the total revenue.

e. What are the expected annual demand and the total revenue according to your recommended price?