Bobby Brady has been nostalgic for his Big Wheel from the 1970s. As a result, he has decided to re-introduce this retro low-riding tricycle with its trademark blue, red, and yellow plastic to a new market. Big Wheels consist of three main parts: the handlebars steering assembly including the one large front wheel, the frame/seat, and two rear wheels. Since the idea's conception, Bobby has been promoting this launch on social media and the videos went viral. As a result, he already has orders for 10,000 Big Wheels so he needs to deliver on these orders. The production requirements are as follows:

	Requirements for Manufacturing
PART	Materials	Time	Storage Space	Cost to Manufacture	Cost to Purchase
	(in sq feet)	(in minutes)	(in cubic feet)
Handlebar, Steering, & Front Wheel	4	13	3	$19	$22
Frame & Seat	5	15	3	$16	$18
Rear Wheel (each)	0.5	6	0.2	$5	$6
Available	130,000	290,000	89,000

Given the unexpectedly large quantity of initial orders, Bobby's manufacturing facility does not have the capacity to produce all of the parts in-house for the 10,000 existing orders. However, he does have the option of outsourcing any of the components from a reliable overseas manufacturer but the cost would be greater than manufacturing in-house as shown on the table. Write up the linear programming model to determine the optimal blend of producing in-house and/or outsourcing each of the major components to satisfy (or exceed) the 10,000 orders at a minimum cost. HINT: Two rear wheels are needed for each unit

Formulate the linear programming problem only. Be sure to define decision variables (HINT: create a decision variable for Handlebar/Steering(Manufacture), Handlebar/Steering (Purchase), Frame/Seat (Manufacture), Frame/Seat (Purchase), etc.), provide objective function, and all constraints. DO NOT SOLVE.