Reference no: EM133052623
An Architect wishes to design the safety deposit room for a bank safe. He plans to place safety deposit boxes approximately 6 feet high by the approximate length of the room's walls, 40 feet (i.e., 240 square feet total space available). The bank has asked him to plan for two sizes of box: large and small. Large boxes consume 1 square foot and will rent for $90 per year. Small boxes consume 0.6 square feet and will rent for $60 per year. The bank has asked for at least 80 large boxes and at least 120 small boxes. The bank hopes to maximize its revenue from safety deposit boxes.
A correct formulation for this problem is provided below:
Let L and S denote the number of units of large and small boxes that the architect's design will provide
MAX Z = 90L + 60S ($)
subject to,
1) Available Space L + 0.6S ≤ 240 square feet
2) Minimum number of large boxes L ≥ 80
3) Minimum number of small boxes S ≥ 120
4) Non-negativity L, S ≥ 0
(b) Using the graphical method, how many of each size should the architect's design provide? What is the annual revenue? 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.
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