Textbook is Optimization Modeling with Spreadsheets. Baker. 3rd Edition.

Question is how do I solve Exercise 6.2

delse gehe at the end objective function coefficients and the right hand side constants are l's, but covering, set packing, and set partitio alizations are also possible, as illustrated in some of the exercises this chapter. based on the ability to represent logical constraints using binary variables. In the In the next chapter, we examine a broader set of integer programming models models, the logical conditions do not seem linear, but they can be expressed in Vine forms with the help of binary variables. EXERCISES 6.1 Callum Communications (Revisited): Revisit Example 6.1. Suppose that the objective at Callum Communications is to minimize the number of employees , rather than to minimize the total cost. (a) What is the minimum number of employees needed at the call center? (b) Does the solution in (a) achieve the minimum salary cost? 6.2 Make or Buy: A sudden increase in the demand for smoke detectors has left Acme Alarms with insufficient capacity to meet demand. The company has seen monthly demand from its retailers for its electronic and battery-operated detectors rise to 20,000 and 10,000, respectively, and Acme wishes to continue meeting demand. Acme's production process involves three departments: Fabrication, Assembly, and Shipping. The relevant quantitative data on produc tion and prices are summarized below. D KUERCISES 221 Monthly Hours Available Department Fabrication Assembly Shipping Hours/Unit (Electronic) 0.15 2000 4200 2500 Hours Unit Battery) 0.10 0.30 0.15 $16.00 $28.00 0.20 0.10 $18.80 $29.50 Variable cost/unit Retail price The company also has the option to obtain additional units from a subcon- tractor, who has offered to supply up to 20,000 units per month in any combination of electronic and battery-operated models, at a charge of $21.50 per unit. For this price, the subcontractor will test and ship its models directly to the retailers without using Acme's production process. (a) Acme wants an implementable schedule, so all quantities must be integers. What are the maximum profit and the corresponding make/buy levels? b) Compare the maximum profit in (a) to the maximum profit achievable without integer constraints. Does the integer solution correspond to the rounded-off values of the noninteger solution? By how much (in percentage terms) do the integer restrictions alter the value of the optimal objective function? 63 Selecting an Investment Portfolio: An investment manager wants to deter- unine an optimal portfolio for a wealthy client. The fund has $2.5 million to invest, and its objective is to maximize total dollar return from both growth and dividends over the course of the coming year. The client has researched eight high-tech companies and wants the portfolio to consist of shares in these firms only. Three of the firms (S1-S3) are primarily software com- panies, three (H1-H3) are primarily hardware companies, and two (C1-C2) a that no more than