Consider two jobs, job 1 and job 2, to be processed on a single machine. it takes 7 days to process job 1, whereas the processing time of job 2 is 4 days. if the production is switched from ob 1 to job 2, then the set-up takes 2 days. on the other hand, if the production is switched from ob 2 to job 1, the set-up time reduces to 1 day. the processing of the jobs cannot start before the beginning of day 3 and both jobs are due at the beginning of day 20. let x1 and x2 be two integer variables representing the start date in days for job 1 and job2 4- two jobs will not be processed concurrently: if job 1 precedes job 2, then the start date of job 2 must be greater than or equal to start date of ob 1 plus the processing of job 1 and the set-up time if job 2 precedes job 1, then the start date of job 1 must be greater than or equal to start date of job 2 plus the processing of job 2 and the set-up time use indicator variable(s) representing the order of processing and mathematically formulate the constraint(s) that are verbally written above using indicator variable(s) and big m(s). calculate the minimum value of m that would work. (hint: what are the ranges for x1 and x2? )

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.]

Why do you think the compensation plans differ at the two firms? in particular, why do you think kaufmann’s pays commissions to salespeople, while parkleigh does not? why does parkleigh offer employees discounts on purchases, while kaufmann’s does not?

David burdick is the ceo of acme bubblegum, a successful public company. as one of the cofounders of the company, burdick has enjoyed speaking and writing about the success of acme bubblegum for several years. typically, he speaks at conferences or directly to the press, but recently, he has been blogging about his firm anonymously. specifically, he defended a recent advertising campaign that was unpopular among consumers and pointedly attacked one of acme bubblegum’s competitors. burdick deeply enjoys his anonymous blogging and believes that none of his readers actually know that he works for acme bubblegum.should burdick be allowed to praise his company’s performance anonymously online? should he be allowed to attack his competitors without disclosing his relationship with the company? how would you feel if the ceo of a company at which you shopped was secretly writing criticisms of his or her competition? how would you feel if you knew a writer for your favorite blog was actually closely involved in a company that the blog discussed? 1. define the ethical issue? 2. who are the primary stakeholders? 3. what are the possible alternatives? 4. how could you evaluate the ethical implications of the alternative actions (use appropriate decision rules)? 5. what action would you recommend and why?