Your school’s band decides to sell cookie dough kits to raise money for a spring field trip. There is a Family Times Cookie Dough kit that you can buy for $7 and sell for $12, and a Baker’s Delight kit that you can buy for $15 and sell for $25. The PTA (Parent – Teacher Association) will lend you $2100 to buy supplies. The company selling you the kits informs you that a school your size can expect to sell at most 220 kits. You should decide : How many of each type of kit should your band purchase to raise the most 11. Move your cursor around in the feasible region and note the various x and y values
for various points within the region. Now, identify a point that has integer values for
its x and y coordinates. Evaluate your objective function using these x and y integer
values. Show your work.
12. Find another point in the feasible region with coordinates that are integer
values. Evaluate the objective function with the x and y coordinates of this new point.
Show your work.
13. Compare the result from part 11with result from part 12. Which pair of coordinates
resulted in a greater value when you evaluated the objective function? Continue
searching for a pair of coordinates in the feasible region that would produce a greater
result when they are used to evaluate the objective function than the coordinates used
in part 11 and part 12. What is the greatest value that can be found for the objective
function? What are the coordinates that produce this value?
14. Are you 100% certain that you have found the coordinates that produce the greatest
value for the objective function? Can you be 100% sure? Explain. What do the
results of part 13 mean within the context of your problem?
15. Consider the context of our linear programming model. Why should we only
consider points with coordinates that are whole numbers?