Matched Problem 1) A manufacturing plant makes two types of inflatable boats-a two-person boat and a four-person boat. Each two-person boat requires 0.9 labor-hour from the cutting department and 0.8 labor-hour from the assembly department. Each four-person boat requires 1.8 labor-hours from the cutting department and 1.2 labor-hours from the assembly department. The maximum labor-hours available per month in the cutting department and the assembly department are 864 and 672, respectively. The company makes a profit of $25 on each two-person boat and $40 on each four-person boat.
(A) Identify the decision variables.
(B) Summarize the relevant material in a table similar to Table 1 in Example 1.
(C) Write the objective function P.
(D) Write the problem constraints and nonnegative constraints.
(E) Graph the feasible region. Include graphs of the objective function for P=$5,000,P=$10,000,P=$15,000, and P=$21,600.
(F) From the graph and constant-profit lines, determine how many boats should be manufactured each month to maximize the profit. What is the maximum profit?
