A factory for the construction of quality furniture has 2 divisions: a machine s

Question

A factory for the construction of quality furniture has 2 divisions: a machine shop where the parts of the furniture are fabricated, and an assembly and finishing division where the parts are put together into the finished product. Suppose that there are 12 employees in the machine shop and 20 in the assembly and finishing division and that each employee works an 8-hour day. Suppose further that the factory produces only two products: chairs and tables. A chair requires 384/17 hours of machine shop time and 480/17 hours of assembly and finishing time. A table requires 240/17 hours of machine shop time and 640/17 hours of assembly and finishing time. Assuming that there is an unlimited demand for these products and that the manufacturer wishes to keep all employees busy, how many chairs and how many tables can this factory produce each day?

Explanation / Answer

Let no. of chairs be x and no. of tables be y. Time in machine shop to build x chairs = 384x/17 hrs Time in assembly shop to build x chairs = 480x/17 hrs Time in machine shop to build y tables = 240x/17 hrs Time in assembly shop to build y tables = 640x/17 hrs Therefore,total time taken in machine shop to build x chairs and y tables: 384x/17 + 240x/17. No. of workers in machine shop = 12 (each have 8 hour days) So total time that can be provided by 12 workers in machine shop = 12 x 8 = 96hrs Now, 384x/17 + 240x/17 = 96 ..........................(i) Similarly, total time taken in assembly shop to build x chairs and y tables: 480x/17 + 640x/17. No. of workers in assembly shop = 20 (each have 8 hour days) So total time that can be provided by 20 workers in assembly shop = 20 x 8 = 160hrs Now, 480x/17 + 640x/17 = 160 ..........................(ii) Solving for x and y we get: 3 chairs and 2 tables per day Ans

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