Q1. How can we determine the number of pecks of apples and pears that should be picked and packed every hour to maximize profit?

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Earnest · Answer

Solving the Linear Program Graphically To maximize profit by picking and packing apples and pears, we can set up a linear programming model. Let x represent the number of pecks of apples and y represent the number of pecks of pears picked and packed every hour. The objective is to maximize profit, given as 4x + 3y. The constraints include total picking and packing time not exceeding 60 minutes and the non-negativity of the number of pecks.  The time constraints for picking and packing apples and pears lead to the inequalities: - For picking apples: 4x + 5y ≤ 60 - For packing apples: 4x + 4y ≤ 60  The non-negativity constraints are: - x ≥ 0 - y ≥ 0  By solving graphically or using a calculator, we find that picking and packing 12 pecks of apples and 6 pecks of pears every hour would result in a profit of $66. This optimal solution is obtained at x = 12 and y = 6. This indicates that 12 pecks of apples and 6 pecks of pears should be picked and packed every hour to maximize profit.

Maximizing Profit by Picking and Packing Apples and Pears

Solving the Linear Program Graphically

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