A car and truck manufacturing plant wishes to prepare a production plan for the next two months so that all demand requirements are met at a minimal cost. There is a limited stock of steel needed for production and at the end of each month, a stock of unsold vehicles can be left.

The data are detailed in the tables below:

1:Amount of steel required for production (ton/unit)

Trucks        1.8

Cars            1.1

Formulate the problem as a linear programming problem in order to minimize costs and answer the following questions using Lindo.

1: What is the cost of the optimal solution?

2: Following an increase in insurance prices, the cost of keeping a car in stock in the first month rose to 140$. Will the optimal solution (the values of the decision variables) change? Will there be a change in the value of the objective function? Choose one answer and then write your explanation

A: The values of the decision variables and the value of the objective function will remain unchanged

B: There will be a change in the values of the decision variables, it is not possible to calculate a change that will apply to the value of the objective function

C: The values of the decision variables will remain unchanged, and the value of the objective function will decrease by $ 3500

D: The values of the decision variables will remain unchanged, and the value of the objective function will increase by $3500

E: The values of the decision variables will remain unchanged, and the value of the objective function will increase by $49,000

3: The demand for trucks in the first month dropped to 200 trucks. How much will the value of the objective function increase?

4: Answer whether the following statement is true or not (it is recommended to make a copy of the original formulation and add the necessary characteristics for the formulation). In order to store trucks, it pays to build a special ramp in the warehouse at a fixed cost of 20,000.

2:production costs($/unit) Trucks Cars 3: Inventory holding costs($/unit) Trucks cars 4: demand (units) trucks cars inventory for steel (tons) Month 1 10,000 8,000 Month 1 100 120 Month 1 450 400 Month 1 2,000 Month 2 11,000 7,000 month 2 120 120 Month 2 350 550 Month 2 2,800