Disney stores recently started selling bobbleheads of The Hulk, and they can’t seem to keep up with the demand. After the attacks on New York and on Sokovia, The Hulk became a popular figure among the public. Even though everyone at first seemed frightened of him and his destructive ways, The Hulk quickly endeared himself to the public by fighting alongside the other Avengers to save the world.
The bobbleheads provide a profit of $3/unit to Disney. There are two types: one says the phrase “Hulk is the strongest one there is” and the other, more popular one says “Hulk Smash!”. In one sales territory, Disney thinks that there is demand for at least 1000 units of the first type and 1500 units of the second. There is enough shelf space for a total of 4000 units.
Disney’s regular bobblehead manufacturer cannot deliver more than 2500 units total, but they can use another company to supply up to 1000 units more of each type. However, that company charges $1 more per unit.
a. Formulate the linear programming model for this problem to help Disney find the optimal procurement strategy to maximize profits. Type the model algebraically into your worksheet but do not solve it.
b. Formulate and solve the dual problem. Using the results of the dual problem only, determine the solution of the primal problem from Part (a).