Question

a company produces mopeds and bicycles. it must produce at least 10 mopeds per month. the company has the equipment to produce only 60 mopeds. it also can produce at most 120 bicycles. the production of mopeds and bicycles cannot exceed 160. the profit for a a moped is $134 and on a bicycle is $20. how many of each should be manufactured per month to maximize profit?

Answer 1

To maximize profit, the number of mopeds and bicycles produced should be determined using linear programming, graphing the constraints, and finding the optimal solution at one of the vertices of the feasible region.

Explanation:

The question relates to linear programming, a mathematical method used for optimizing a given objective function, subject to constraints. To maximize profit in this scenario, we need to determine the number of mopeds and bicycles to produce each month.

Let's define x as the number of mopeds and y as the number of bicycles. The profit function to maximize is P = 134x + 20y. The constraints are as follows:

• x ≥ 10 (at least 10 mopeds)
• x ≤ 60 (no more than 60 mopeds)
• y ≤ 120 (no more than 120 bicycles)
• x + y ≤ 160 (total production not exceeding 160 units)

To find the solution, we could graph the constraints and locate the vertices of the feasible region. The optimal solution (number of mopeds and bicycles to maximize profit) will be at one of these vertices, as per the fundamental theorem of linear programming.