The RBC (Royal Bank of Canada) uses online banking to market two new banking products. The first product is a home risk insurance that allows buyers to default for up to 6 months on their mortgage payments. The second is a guaranteed mortgage fund that buyers may purchase to leverage their funds without increasing their debt loads. The RBC expects to make profit contributions of $20 per unit on the home risk insurance instrument, and $8 per unit on the guaranteed mortgage fund. The bank has a policy that at least 50% of total sales of the two products are home risk insurance instruments. The bank is now determining sales quotas for its online offerings to maximize total expected contribution to profits based on the product resource requirements, as follows:
a) Graph the constraint lines and mark them clearly with the numbers (1), (2), (3) and (4) to indicate which line corresponds to which constraint. Darken the feasible region. (12 points)
(b) Determine the optimal solution that will maximize the total expected contribution to profits. Report the solution in a managerial statement (i.e. describe verbally the optimal solution and its profit). Provide all necessary calculations to justify your answers. (7 points).
(c) Which constraint(s) is (are) redundant? (3 points)
(d) Will there be excess capacity in the Data Management resource? Justify. (3 points).
Resource Requirements per Product Offering (Hours per Unit) Bank Home Risk Guaranteed Resource Availability Department Insurance (HRI) Mortgage (GM) (Hours) Legal 6 4 4,800 Data Management 1 2 2,000 Policy Claims 3 0 1,800 A correct formulation for this problem is provided below: Let HR] and GM denote the number of units of Home Risk Insurance instruments and Guaranteed Mortgage units to sell online, respectively. MAXZ = 20 HRI + 8 GM ($) subject to, 1) Legal Hours 6 HRI + 4 GM S 4,800 hrs 2) Data Mgt Hours 1 HR] + 2 GM S 2,000 hrs 3) Policy Claims 3 HRI S 1,800 hrs 4) Ratio Policy Limits 0.5 HRI - 0.5 GM 2 0 5) Non-negativity HRI, GM 2 0
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