Instructions:

The LP formulation consists of variable definition, objective function, and constraints.

You need to define the decision variables clearly and precisely

You do not need to simply the obj function and constraints. You are not required to solve the problem either.

A toy producer produces two similar toys, "Gadget" and "Widget". "Gadget" is composed of 60 sticks and 30 connectors, while "Widget" is composed of 30 sticks and 20 connectors. For this season, the toy producer has a supply of only 60,000 connectors and 93,000 sticks. The profit contributions are $5 and $3 per toy, respectively, for "Gadget" and "Widget". According to the forecast, the total demand for the two toys is under 1000 units. In addition, the producer would like to produce more Gadget than Widget based on the demand pattern. There are also 100 units and 200 units of customer pre-orders for Gadget and Widget, respectively. Both pre-orders need to be satisfied based on the contractual requirement. Formulate a linear program for this producer to determine the number of each toy to be produced to maximize its total profit.