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Math · Advanced Math
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1. (Production problem) A small mannfacturing plant makes three types of inflat- boats: one person, two-person and four-person models. The production of h boat requires the services of three departments as shown in the table below The cutting, assembly and packaging departments have available a maximum of 190, 280 and 310 work hours per week respectively. The manufacturer would like to know how many boats of each type must be produced each week for the eac plant to operate at full capacity Required hours per boat one person two son four person cutting assembly packaging (a) Set up the problem as a system of equations (b) Solve by the five-step Gauss-Jordan elimination algorithm 2. (Heat conduction problem) A structure composed of metal bars is shown below The temperature of the end of each bar is given in the figure. The temperatures at the junctions are x1-22 and 13 64 32 (a) Using the rule that the temperature at each junction is the average of the three adjacent temperatures, set up a system of equations for the junction temperatures. (b) Use the five-step Gauss-Jordan elimination algorithm to solve for the tem- peratures.

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