Suppose that separable programming has been applied to a certain problem (the “original prob-lem”) to convert it to the following equivalent LP model maxz=5x11+4x12+2x13+4x21+x22s. t. 3x11+3x12+3x13+2x21+2x22≤252x11+2x1 2+2x13−x21−x22≤10x11≤2x12≤3x21≤3x22 ≤1x11,x12,x13,x21,x22≥0
1. What was the mathematical model for the original problem? Answer this by plotting the profit graph for each of the original activities and then writing the optimization model (do only the step number 5 of the modeling process) for the original problem in terms of the original decision variables (Hint: Pay special attention to the constraints)(50 points).

Suppose a firm faces a fixed price of output, 푝푝= 1200. the firm hires workers from a union at a daily wage, 푤푤, to produce output according to the production function 푞푞= 2퐸퐸12. there are 225 workers in the union. any union worker who does not work for this firm is guaranteed to find nonunion employment at a wage of $96 per day. a. what is the firm’s labor demand function? b. if the firm is allowed to choose 푤푤, but then the union decides how many workers to provide (up to 225) at that wage, what wage will the firm set? how many workers will the union provide? what is the firm’s output and profit? what is the total income of the 225 union workers? c. now suppose that the union sets the wage, but the firm decides how many workers to hire at that wage (up to 225). what wage will the union set to maximize the total income of all 225 workers? how many workers will the firm hire? what is the firm’s output and profit? what is the total income of the 225 union workers? [hint: to maximize total income of union, take the first order condition with respect to w and set equal to 0.]

Over the past year, three of the star salesmen at family resorts international's corporate office have been lured away to competitors. on top of that, karina, the general manager of the sales department, has noticed that most employees come in, do their jobs, and leave. family resorts offers a good salary, benefits, and tuition reimbursement, as well as a number of development and training programs. most employees seem contented enough, but karina would like to do something to increase the level of engagement among her staff. what do you think karina should do?

Spartan credit bank is offering 7.5 percent compounded daily on its savings accounts. you deposit $5,900 today. a. how much will you have in the account in 4 years? (use 365 days a year. do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.) b. how much will you have in the account in 12 years? (use 365 days a year. do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.) c. how much will you have in the account in 19 years?