During the next four quarters, Dorian Auto must meet (on time)the following demands for cars: 4000 in quarter 1; 2000 in quarter2; 5000 in quarter 3; 1000 in quarter 4. At the beginning ofquarter 1, there are 300 cars in stock. The company has thecapacity to produce at the most 3000 cars per quarter. At thebeginning of each quarter, the company can increase (but notdecrease) its production capacity. It costs $100 to increaseproduction capacity by one unit. For example, it would cost $10,000to increase production capacity from 3000 cars per quarter to 3100cars per quarter. It also costs $40 per quarter to maintain eachunit of production capacity (whether it is used or not). Thevariable cost of producing a car is $2000. A holding cost of $150per car is assessed for each quarter’s ending inventory. It isrequired that at the end of quarter 4, plant capacity must be atleast 4000 cars.       

(1) Determine how to minimise the total cost incurred during thenext four quarters.

There is a concern that due to rising material and labour costs,the variable cost in the fourth quarter may increase by 10%.

(2) Should you change your production plan if you believe thisincrease will occur?

(3) What would you do if you believed that there would be a 20%increase in variable costs in the fourth quarter?

Use both MATLAB Optimisation Toolbox and Excel Solver to solvethe problems