The Polar Sports company manufactures

both snowboards and skis. It takes 8

hours to manufacture a snowboard and

10 hours to manufacture a set of skis.

There are 400 hours of labor available

each week for production. Due to

demand, they must produce at least 15

snowboards. Snowboards profit $55

each and skis profit $80 each. How

many of each should they produce in a

week to maximize their profit?

15 snowboards, 28 sets of skis

Step-by-step explanation:

There is only one resource involved: hours of labor. We can figure the most profitable way to allocate that resource by looking at the profit it can generate.

Profit from making snowboards is

... ($55 profit) / (8 hours labor) = $6.875 per hour

Profit from making skis is

... ($80 profit) / (10 hours labor) = $8.00 per hour

Clearly, making skis is a better use of the labor hours. However, we must satisfy the contraint to produce at least 15 snowboards. The most profitable use of time is to produce 15 snowboards, requring 15*8 = 120 hours, and spending the remaining 280 hours producing 28 sets of skis.