decision analysis

3. SecureLock has a recent order for 2400 door lock units for a townhome complex. Each lock unit consists of three components: the knob and face plate, the actual lock itself, and a set of two keys. Although the processes used in the manufacture of the three components vary, there are three areas where the manager is concerned about the availability of resources. These three areas, their usage (in minutes) by the three components, and their availability are detailed in the table. Resource Alloying Machining Finishing Knob and Plate 12 18 15 Lock 5 20 5 Key (each) 1 10 1 Available 15000 units 36000 minutes 12000 minutes SecureLock may not have the resources to fill this contract. In that case, SecureLock can purchase the components from a subcontractor, who can provide an unlimited number of each of the three components, quotes the prices below. Component Cost to Manufacture Cost to Purchase Knob and Plate 6.00 10.00 Lock 4.00 I 9.00 Keys (set of 2) 0.50 1.00 Develop a linear programming model to tell SecureLock how many of ench component should be manufactured and how many should be purchased in order to provide 2400 door lock units at the minimum cost. You should clearly show 1) decision variables, 2) objective function, and 3) constraints. (25pt) Type your answer below!!!!! Total Cost