Question

A manufacturer of bicycles builds 1-, 3- and 10-speed models. The bicycles are made of both aluminum and steel. The company has available 41,960 units of steel and 35,072 units of aluminum. The 1-, 3-, and 10-speed models need, respectively, 10, 15 and 20 units of steel and 12,8 , and 16 units of aluminum. The company makes $4 per 1 -speed bike, $6 per 3-speed, and $16 per 10 -speed. How many of each type of bicycle should be made in order to maximize profit?

Answer 1

To maximize profit, we need to determine the number of each type of bicycle that should be made. We can use linear programming techniques such as the simplex method or graphing the feasible region to find the optimal solution.

Step-by-step explanation:

To maximize profit, we need to determine the number of each type of bicycle that should be made. Let's assume that x represents the number of 1-speed bikes, y represents the number of 3-speed bikes, and z represents the number of 10-speed bikes. The objective is to maximize the profit function P = 4x + 6y + 16z, subject to the constraints:

10x + 15y + 20z ≤ 41,960 (constraint for steel)

12x + 8y + 16z ≤ 35,072 (constraint for aluminum)

x, y, z ≥ 0 (non-negativity constraints)

To solve this problem, we can use linear programming techniques such as the simplex method or graphing the feasible region to find the optimal solution.