Credo Carpet Company produces three carpet designs: Coracle, Alpine and Fantasia, which are sold OR 30, OR 40 and OR 65 each, respectively. The carpets are made from three different types of wool - plain, flecked, and dyed, supplied on 10 km drums at OR IXY, OR 40 and OR 10 per drum, respectively. XY refers to the first two digits of your student ID starting from the right. The Coracle requires 0.5 km of plain, 0.2 km of flecked, and 0.2 km of dyed wool. The Alpine requires 0.7 km of plain, 0.2 km of flecked, and 0.2 km of dyed wool. The Fantasia requires 0.2 km of plain, 0.5 km of flecked, and 1 km of dyed wool. There are currently 5 drums of plain wool, 2 drums of flecked, and 3 drums of dyed wool available. Besides the cost of the materials, the other production costs are estimated to OR 4, OR 7 and OR 10 per unit of Coracle, Alpine and Fantasia, respectively. 1. Formulate the linear programming model to help Credo Carpet Company develop a production plan that maximizes the overall profit. 2. Use Excel to solve the problem and provide the corresponding sensitivity report. 3. How many of each type of carpet should be produced and what profit will this generate? 4. Which constraints are binding? Explain. 5. Three additional drums of plain wool can be provided by the supplier at a cost of OR 50 per drum. Should Credo purchase this wool and, if so, how many drums should they purchase? Explain. 6. What is the range of optimality for the coefficient of Alpine? 7. In the optimal solution, one of the carpets is not produced. At what profit would Credo start producing this carpet? How can such a solution be implemented in practice? Explain. 8. If the price of wool increases with OR 20 per drum, will the optimum production plan change and what will be its effect on the optimal profit? Justify your answer. 9. Due to global supply difficulties, the suppliers of wool have suggested an adjustment plan for the supply of wool, where the flecked supply is decreased to 4 km and the dyed is increased by 1 km. How would such a change affect Credo's overall profit? Justify your answer.