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# Applied Math 118 &amp;quot;- Linear programming application The BOATLIFT company manufactures two different sizes of boat lifts . Each size requires...

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Applied Math 118 "- Linear programming application The BOATLIFT company manufactures two different sizes of boat lifts . Each size requires some time in the Welding and Assembly Department and some time in the Parts and Packaging Department . Base Case: The smaller lift requires 3/4 hour in Welding and Assembly, and 1 and 2/3 hours in Parts and Packaging . The larger lift requires 1 and % hour in Welding and Assembly, and 1 hour in Parts and Packaging. The factory has 156 hours/day available in Welding and Assembly and 174 hours in Parts and Packaging. The demand for the lifts is at most 90 large models/day and at most 100 small models/day; profit is \$50 fo r each large lift and \$25 for ~ h small lift. :=::: : Let x be the number of small lifts produced and y be the number of large lifts produced. We would like to decide how many of each type should be produced each day to maximize profits. You need to follow the step-by-step process outlined below : o # 1: Write down all constraints using x and y as the number of small and large lifts produced 0# 2: Using the graph paper attached or your own graph paper, graph all constraints and shade the feasible region in bright yellow (graph # 1). o # 3 : Calculate the coordinates of each of the corner points and summarize in a table. 0# 4: Write down the objective function Z o # 5: Calculate the value of the objective function at each corner point and summarize in a table 0#6 : State where the optimal solution(s) is (are). Alternate Scenarios : as we change one or more of the initial conditions, keep all other conditions the same as in the base case . You should redraw the graph for each new alternate scenario . Alternate Scenario 1
o # 7: Assuming that the max demand on the larger lift is only 50, while the max demand on the smaller lift is unchanged at 100, find out the optimal solution(s) . Redraw the graph (graph # 2), calculate the value of the objective function at each corner point and state the new optimal solution(s). Alternate Scenario 2 (back to the base case) o # 8: Assuming that the profit for each large lift is \$75 instead of \$50, find out the new optimal solution(s) by calculating the objective function for each corner point (graph # 3) . Alternate Scenario 3 (back to the base case) 0# 9 : Assuming that the max demand on the larger lift is only 50 and that the profit for each large lift is \$75 instead of \$50, find out the new optimal solution(s) by calculating the objective function for each corner point (graph # 4). Math 118

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