The Tiny Toy Company makes three types of new toys: the tinytank, the tiny truck, and the tiny turtle. Plastic used in one unitof each is 1.5, 2.0 and 1.0 pounds, respectively. Rubber for oneunit of each toy is 0.5, 0.5, and 1.0 pounds, respectively. Also,each tank uses 0.3 pounds of metal and the truck uses 0.6 pounds ofmetal during production. The average weekly availability forplastic is 16,000 pounds, 9,000 pounds of metal, and 5,000 poundsof rubber. It takes two hours of labor to make one tank, two hoursfor one truck, and one hour for a turtle. The company allows nomore than 40 hours a week for production (priority #1). Finally,the cost of manufacturing one tank is $7, 1 truck is $5 and 1turtle is $4; a target budget of $164,000 is initially used as aguideline for the company to follow.

a) Minimize over-utilization of the weekly available supply ofmaterials used in making the toys and place twice as much emphasison the plastic (priority #2)

b) Minimize the under and over-utilization of the budget. Maximizeavailable labor hour usage (priority #3).

Formulate the above decision problem as a single linear goalprogram. Clearly identify your achievement vector (i.e., hierarchyof priority levels for the goals). Do not solve.