1. a. Suppose the class recommend that no fewer than 5 but no more than 20 pizzas should be purchased for resale during their fundraiser. Draw a graph below that represents the information on an xy-coordinate plane where x represents the number of pizzas and y represents the number of six-packs of soda.
b. If point C represents any point in the shaded region, describes its possible range of
d. Suppose the class recommended that no fewer than 10 but no more than 40 six-packs of soda
be purchased. Represent the range of six-packs that might be ordered on your graph above.
e. Use a color (i.e. colored pencil) to graph the intersection of the region that describes the
recommended range of pizzas with the region that describes the recommended range of
six-packs of pop.
f. Write inequalities to describe the set of feasible solutions.
g. In your inequalities for Part a, did you use the symbols < and > or the symbols
< and >? Explain your choice.
2. The Class has decided to start concession sales using only pizza and soda. We estimate a
reasonable cost for each pizza (from the local store) to be $7.00 and the cost of a six-pack of soda to be $12.00.
a. Write inequalities to represent the number of pizzas that can be purchased for $400 or less, where x represent number of pizzas.
b. Write inequalities to represent the number of six-packs that can be purchased for $400 or less, where y represents number of six- packs.
c. Graph these inequalities on a two-dimensional coordinate system where y represents
the number of six-packs and x represents number of pizzas.
d. In Part a and b, you assumed that the entire $400 could be spent on the either pizza or pop. Write an inequality in which $400 is the limit for the total cost of both items.
e. Graph this constraint on the coordinate system above. Label the feasible region on your graph and explain what it represents in this situation.
f. Are all points in this feasible region valid for this real-world situation? Explain why or why not? (Think back to all constraints that have been stated previously in this activity.)
3. After creating a third graph with all the constraints discussed (price and quantity), determine the coordinates of the corner points of the feasible region and describe what each of them represent in the context.