Football Fanatics, Inc. makes three types of footballsFootball Fanatics

Football Fanatics, Inc. makes three types of footballs $-$ the Pee Wee, the College Canon, and the Pro

Player. The labor and materials requirements for each football are shown in the table below with

information regarding the maximum amount of labor hours available $($for a given activity$)$ and the

maximum amount of each material available.

The firm purchases only as much of the three materials $($rubber$,$ leather, and stitching$)$ as it uses

at the prices shown in the table. It wants the Pro Player to comprise at least $10\%$ of all the

footballs it produces and sells. In addition, the number of Pro Player and College Canon

footballs $($in total$)$ must not be more than $50$ percent of the total number of footballs produced

and sold.

$(1)$ How many of each type of football should be produced to maximize its profits, subject to the

availability and sales$-$planning constraints given? $($fractional answers are OK$)$

$(2)$ How does this result differ when integer decisions $($i$.$e$.,$ whole numbers of footballs$)$ are assumed

necessary for planning estimates? Provide the new decisions and the final profit.