Mr smart is the manager of the firm with two plants a and b

Question

Assignment

Mr. Smart is the manager of the firm with two plants A and B, which manufacture the products to satisfy two markets 1 and 2. The production capacity of the plant and B are 100 and 120, and the demands at market 1 and 2 are 110 and 130. Mr. Smart decides to use an optimization model to find out the best production and delivery plan to maximize the total net profit. In this model, he uses X_i,j,i=A,B, and j=1,2, to indicate the amount of products produced at plant i and delivered to market j. Mr. Smart also uses the following two constraints in the optimization model to represent the demand constraints at markets 1 and 2:

X_A,i+X_B,1= 110; X_A,2+X_B,2 = 130.

If Mr. Smart uses the above two constraints in his model to solve the optimal production and delivery plan, is there any potential problem? If yes, explain why and suggest what adjustments you would like to make; if no, please also explain why.