Please Formulate a detailed model. Don't forget to define the variables and note the units of any quantities considered. Do not solve. Thank you very much!

10. Using Material C, a firm produces Commodities A and B. The requirements for the manufacture of a unit of each are as follows: Commodity Labor (hr) C(units) 3 5 B 2 8 The firm has available each month 400 hr of labor at a cost of $12/hr and up to an additional 100 hr of overtime at $18/hr. The firm has 3500 units of C in stock but can obtain no more. For the next 3 months, up to 100 units each of A and B can be sold each month at the following prices per unit: Price of B ($) Price of A ($) 60 62 64 Month 1 Month 2 Month 3 50 58 65 The firm's warehouse, with a 3000-ft capacity, can store units of A and B pro- duced during one month for sale during a later month, but it must also store all the unused units of C. One unit of A requires 8 ft of space, one unit of B 9 ft of space, and one unit of C 0.8 ft of space. At the end of the 3-month period, any units of C left in stock must be disposed of at a cost of $1.50/unit. Determine an operating schedule that maximizes profit