Chapter 4.3, Problem 26E

PRODUCTION SCHEDULING Wayland Company manufactures two models of its twin-size futons, standard and deluxe, in two locations, I and II. The maximum output at Location I is $600/\text{week}$, whereas the maximum output at location II is $400/\text{week}$. The profit per futon for standard and deluxe models manufactured at Location I is $\$30$ and $\$20$, respectively; the profit per futon for standard and deluxe models manufactured at Location II is $\$34$ and $\$18$, respectively. For a certain week, the company has received an order for $600$ standard models and $300$ deluxe models. If prior commitments dictate that the number of deluxe models manufactured at Location II not exceed the number of standard models manufactured there by more than $50$, find how many of each model should be manufactured at each location to satisfy the order and at the same time maximize Wayland’s profit. What is the maximum profit?