Question

To sell 300 notebook and 120 pens quickly, a store decided to create two types of gift sets. One set is to include 2 notebooks and 1 pen, and the other will consist of 1 pen and 3 notebooks. First set will be sold for $8. While the second one is to cost $11.50. It is unprofitable for the store to sell less than 20 of any gift set. How many gift sets of each type does store need to sell to obtain the biggest possible income?

Answer 1

If there are
x sets of 2 notebooks and 1 pen
y sets of 3 notebooks and 1 pen
Then you want to maximize p = 8x + 11.50y
subject to the constraints
2x+3y <= 200
x+y <= 120
x >= 20
y >= 20
So now just graph the region and check p at each vertex, as usual.

Answer 2

2x+3y <= 200

300 I think :(

Answer 3

the curse of the typo strikes again ...
good catch
But I'm sure Phoenix caught it too, right? ... right?

Answer 4

I have the same question, but I couldn't understand what you mentioned above oobleck

Answer 5

graph each of the lines of constraint, and shade the areas that satisfy the inequalities. The intersection of all those shaded area is your region of interest. The objective function p will achieve its maximum value at one of the vertices of the shaded region. So evaluate p at each vertex, plugging in the x,y values there. Pick the vertex where p is the largest. In this case, select the closest integer values, since pens and notebooks don't come in fractional amounts.

If this still makes no sense, review linear programming and maximizing objective functions. Many examples and explanations are easily found online.

Answer 6

Got it, thanks :)