Question

Top Brass Trophy Company, makes large championship trophies for youth athletic teams. At the moment they are planning production for fall sports: football and soccer. Each football trophy has a wood base, an engraved plaque, a large brass football on top, and returns $12 in profit. Soccer trophies are similar except that a brass soccer ball is on top, and the unit profit is only $9. Since the football has an asymmetric shape, its base requires 4 board feet of wood; the soccer base requires only 2 board feet. At the moment there are 1000 brass footballs in stock, 1500 soccer balls, 1750 plaques, and 4800 board feet of wood.

Required:
a. Define your decision variables and variable restrictions.
b. Build and present your linear programming model.
c. If you can, solve your linear programming model by graphical method. Otherwise, state your reason. Note that you can derive an optimal solution exactly by solving related equations.
d. If the number of available plaques is 200, modify your model and solve it again.

Answer 1

a) maximize 12F + 9S

where:

F = football trophies

S = soccer trophies

b) constraints:

wood ⇒ 4F + 2S ≤ 4800

plaques ⇒ F + S ≤ 1750

brass footballs ⇒ F ≤ 1000

brass soccer balls ⇒ S ≤ 1500

c) using solver, the optimal solution is 650F + 1100S = $17,700

d) plaques ⇒ F + S ≤ 200, then

optimal solution is 200F = $2,400