0

A small tailors’ company wants to use at least 130 yards of fabric to sew evening skirts and dresses. A dress requires 4 yards of fabric and the production of a skirt will need 3 yards. Research shows that they will be able to sell at most three times as many skirts as dresses . A dress will take 10 hours to produce and a skirt will take 1 hour. They can assign to this work no more than 286 hours. Each dress will sell for $540, and each skirt will sell for $180. How many skirts should they sew to maximize the profit?

Click this - https://www.desmos.com/calculator/0a8b743iyi

It will show the equations I made with it graphed. I need help here. What should I do now?

Also - C(x,y) = 540x+180y (right)?

user318237
  • 11

1 Answers1

1

The whole point of such a problem is that the point that maximizes (or minimizes) a linear function on a convex polygon must occur at one of the vertices of the polygon. So your first job is to determine the vertices. By converting your inequalities to equations, x= 0, y= 0, 3y= x, 4x+ 3y= 130, and 10x+ y= 286, we have the equations of the boundaries of the polygon. The vertices are where those lines intersect which you can find by solving pairs of those equations. For example, "x= 0, y= 0" tells us immediately that one vertex is (0, 0). "x= 0, 4x+ 3y= 130" tells us that (0, 130/3)= (0, 43.333...) might be a vertex but we also have "x= 0, 10x+ y= 286" gives (0, 286). Since 130/3< 286, the vertex is (0, 130/3).

After finding all the vertices, evaluate the target function, 540x+ 180y, at each vertex to see which gives the largest value.

user247327
  • 18,710