Leary Chemical manufactures three chemicals: A, B, and C. These chemicals are produced via two production processes: 1 and 2. Running process 1 for an hour costs $4 and yields 3 units of A, 1 of B, and 1 of C. Running process 2 for an hour costs $1 and produces 1 unit of A and 1 of B. To meet customer demands, at least 10 units of A, 5 of B, and 3 of C must be produced daily. Processes cannot be run simultaneously, and total number of operational hours is limited to 12 hours. Construct an LP model to determine a daily production plan that minimizes the cost of meeting Leary Chemical’s daily demands.

Scenario A (Question 1-3) Acme engineering is a general light engineering company that specializes in metallic fixtures and fittings. It manufactures various products to customer order, and also has long term contracts to supply manufactured products to other companies. Acme is a "jobbing shop" involving craftspeople making specialized complete products - it is not a production line operation. The craftspeople work on early (6am-2pm) and late (2pm-10pm) shifts 5 days a week, and sometimes do overtime on Saturdays.. The factory is always closed on Friday. Each shift has a supervisor. The management team consists of the Managing Director, Accountant and Sales Manager. They are assisted by two Administrative Assistants who work Sunday to Thursday, 8.30am to 5.30pmS pe cify indicators for the conligency The management team has decided that, in order to become more competitive, it needs more and better information on the costs involved in manufacturing: It wants to build up a database of…

2.

Portfolio manager Max Gaines needs to develop an investment portfolio for his clients who are willing to accept a moderate amount of risk. His task is to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the portfolio maximizes the expected return but provides an annual return of no less than 3%. for each of the following scenarios. Annual Returns (Planning Scenarios): mutual fund yr 1 yr 2 yr 3 yr 4 international stock 22.37 26.73 6.46 -3.19 low-cap blend 14.88 18.61 10.52 5.25 mid-cap blend 19.45 18.04 5.91 -1.94 small-cap blend 13.79 11.33 -2.07 6.85 intermediate bond 7.29 8.05 9.18 3.92 Formulate the appropriate linear program for this situation. (state the objective function, the decision variables, and the constraints)