Calculations must be done in word. Every step must be shown 1. Only formulate the problem: a) PharmaPlus operates a chain of 30 pharmacies. The pharmacies are staffed by licensed pharmacists and pharmacy technicians. The company currently employs 85 full-time equivalent pharmacists (combination of full time and part time) and 175 full-time equivalent technicians. Each spring management reviews current staffing levels and makes hiring plans for the year. A recent forecast of the prescription load for the nest year shows that at least 250 full-time equivalent employees (pharmacists and technicians) will be required to staff the pharmacies. The personnel department expects 10 pharmacists and 30 technicians to leave over the next year. To accommodate the expected attrition and prepare for future growth, management stated that at least 15 new pharmacists must be hired. In addition, PharmaPlus's new service quality guidelines specify no more than two technicians per licensed pharmacist. The average salary for licensed pharmacists is $40 per hour and the average salary for technicians is $10 per hour. Determine a minimum-cost staffing plan for PharmaPlus. How many pharmacists and technicians are needed? b) You have $12,000 to invest, and three different funds from which to choose. The municipal bond fund has a 7% return, the local bank's CDs have an 8% return, and the high-risk account has an expected (hoped-for) 12% return. To minimize risk, you decide not to invest any more than $2,000 in the high-risk account. For tax reasons, you need to invest at least three times as much in the municipal bonds as in the bank CDs. Assuming the year-end yields are as expected, what are the optimal investment amounts? 2. The following network is given: a) How many variables must be used? ....................... b) How many constraints (except non-negativity constraint) will be given? .................... c) Give a constraint corresponding to node 3. d) Give a constraint corresponding to node 8. e) Do we need to apply a dummy node? Explain your answer. f) What kind of change in original formulation must be done if a warehouse in Louisville cannot store more than 400 units