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?

Data from Table 1 Example 1

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Table 1 Cutting department Assembly department Profit per tent Labor-Hours per Tent Standard Model 1 3 $50 Expedition Model 2 4 $80 Maximum Labor-Hours Available per Day 32 84