Question

The Rocky Mountains Ski Company makes skis and snowboards . Skis require 12 hours of fabrication and 1 hour of finishing . Snowboards require 10 hours of fabrication and 1 hour for finishing. Skis have a profit of $60 & snowboards have $55 profit. If there are 420 labor hours available for fabrication and 36 hours for finishing. How many skis and snowboards should be made to maximize profit.

Answer 1

To maximize profit, we need to determine the number of skis and snowboards that should be made. The maximum profit is achieved when 30 skis and 6 snowboards are made.

Step-by-step explanation:

To maximize profit, we need to determine the number of skis and snowboards that should be made. Let's assume x represents the number of skis and y represents the number of snowboards.

From the information given, we have the following constraints:

• 12x + 10y ≤ 420 (fabrication hours)
• x + y ≤ 36 (finishing hours)
• x, y ≥ 0 (non-negative)

The profit function is given by P = 60x + 55y. To maximize profit, we need to find the maximum value of P subject to the given constraints. This is a linear programming problem, and we can use a graphical method or an algebraic method (such as the simplex method) to solve it.

Using the graphical method, we can plot the feasible region (the region bounded by the constraints) and find the corner points. We then evaluate the profit function at each corner point to find the maximum value.

After solving, we find that the maximum profit is achieved when 30 skis and 6 snowboards are made.