A firm faces a deterministic, constant demand rate D per unit time. He purchases units from his supplier at cost c to satisfy this demand (all demand must be met). The supplier instantly delivers the ordered quantity. Every time the firm places an order from his supplier, he incurs a fixed cost of A. He also incurs a holding cost h per unit of inventory kept per unit time. He determines his order quantity that minimizes his total cost per unit time. The firm is facing a regulatory restriction on his carbon emissions. His (average) total emissions per unit time cannot exceed the cap C. The firm did make an analysis on his operations and their GHG emissions and noticed that there are three sources of emissions. He generates an amount of A each time he places an order from his supplier. Additionally, he generates an amount of c emissions per unit purchased. Emissions from holding inventory depends only on the maximum amount of inventory held, with an estimated amount h per unit per unit time. (a) Formulate the firms problem. Clearly state the objective function and the constraint(s). (b) Find the firms optimal order quantity in this constrained problem. Show all your work.