Company A has agreed to supply the following quantities of spe- cial lamps to Company B during the next 4 months: Month January February 150 Units 160 March April 225 180 Company A can produce a maximum of 160 lamps per month at a cost of $35 per unit. Additional lamps can be purchased from Company C at a cost of $50 per lamp. Company A incurs an inventory holding cost of $5 per month for each lamp held in inventory. (a) Formulate the problem that Company A is facing as a linear programming problem. (b) Solve the problem using a linear programming package. (c) Company A is considering some preventive maintenance during one of the first three months. If maintenance is scheduled for January, the company can manufacture only 151 units (instead of 160); similarly, the maximum possible production if maintenance is scheduled for February or March is 153 and 155 units, respectively. What maintenance schedule would you recommend and why? (d) Company D has offered to supply up to 50 lamps (total) to Company A during either January, February or March. Company D charges $45 per lamp. Should Company A buy lamps from Company D? If yes, when and how many lamps should Company A purchase, and what is the impact of this decision on the total cost? (e) Company C has offered to lower the price of units supplied to Company A during February. What is the maximum decrease that would make this offer attractive to Company A? (f) Because of anticipated increases in interest rates, the holding cost per lamp is expected to increase to $8 per unit in February. How does this change affect the total cost and the optimal solution? (g) Company B has just informed Company A that it requires only 90 units in January (instead of 150 requested previously). Calculate upper and lower bounds on the impact of this order on the optimal cost using information from the optimal solution to the original problem.