Question 238271: Planning a fundraiser your club plans to raise money by selling two sizes of fruit baskets. The plan is to buy small baskets for $10, and sell them for $16 and to buy large baskets for $15 and sell them for $25. The club president estimates that you will not sell more than 100 baskets. Your club can afford to spend up to 1200 dollars to buy the baskets. Find the number of small and large fruit baskets you should buy in order to maximize profit. Let x be small baskets and y be large.
Objective function: P= _x+_y
Constraints: (really need help with)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Your objective function is not quite right. Since you want to maximize profit, the profit on a small basket is 16 - 10 = 6, and on a large basket is 25 - 15 = 10, so your objective function needs to be:
You won't sell more than 100 baskets, per Pres. estimate so:
You can't spend more than $1200 procuring the baskets, and smalls cost 10 and larges cost 15, so:
You can't sell less than zero of either kind of basket, so:
and
And, since it is highly unlikely that anyone will buy a fractional part of a basket of either size both quantities must be integers:
Your area of feasibility, based on the above constraints is integer values where the ordered pair (x, y) is in the region bounded by the quadrilateral with vertices (0, 0), (100,0), (60, 80), and (0,80). You need to graph all of the constraints and solve the system:
to find these points for yourself.
There is an operations research theorem that says the optimum point will be at a vertex of the area of feasibility. So, just plug the vertex values into the objective function and see which one gives you the biggest answer.
John
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