Photo Chemicals produces two types of photographic developing fluids. Both products cost Photo Chemicals $1 per gallon to produce. Based on an analysis of current inventory levels and outstanding orders for the next month, Photo Chemicals management has specified that at least 30 gallons of product A and at least 20 gallons of product B must be produced during the next 2 weeks. Management has also stated that an existing inventory of highly perishable raw material required in the production of both fluids must be used within the next 2 week. The current inventory of perishable raw material is 80 pounds. While more of this raw material can be ordered if necessary, any of the current inventory that is not used within the next 2 weeks will spoil hence, the management requirement that at least 80 pounds be used in the next 2 weeks. Furthermore, it is known that product A requires 1 pound of this perishable raw material per gallon and product B requires 2 pounds of the raw material per gallon.

a) Because Photo Chemicals objective is to keep its production cost at the minimum possible level, the firms management is looking for a minimum-cost production plan that uses all the 80 pounds of perishable raw material and provides at least 30 gallons of product A and at least 20 gallons of product B. Determine the minimum cost solution.

b) Due to some technical problems, management of Photo Chemical has to change their decision to provide at least 30 gallons of product A to 20 gallons. But there is no change for minimum production of product B. Besides that, the cost of Product B increase to $2.3 per gallon to produce but there is no changes for the cost of product A. Determine the new minimum cost solution.