Plastic Chairs

Plastic Chairs manufactures plastic lawn chairs using a combination of new and recycled plastic.

Varying amounts of each type of plastic can be used to produce a batch of $100$ chairs. The following table lists the various combinations of recycled and new plastic required to produce one batch of

$100$ chairs.

$320$ Chapter $7$

Pounds of New and Recycled Plastic Required

to Manufacture One Batch of $100$ Chairs

Pounds of New

Plastic

Pounds of

Recycled Plastic

$2072$

$2460$

$3048$

$3245$

$3640$

$4036$

$4532$

$4830$

$6024$

$7220$

New plastic costs $$16$ per pound and recycled plastic costs $$10$ per pound. The manager of

the chair manufacturing department receives a bonus based on minimizing the cost per batch

of $100$ chairs.

Required:

a$.$ What combination of new and recycled plastic will the manager of the chair manufacturing

department choose?

b$.$ Overhead $($including plant administration, utilities, property taxes, and insurance$)$ is allocated to the chair manufacturing department based on the number of pounds of recycled

plastic used in each batch. For each pound of recycled plastic used, the chair manufacturing department is charged $$30$ of plant overhead. What combination of new and recycled

plastic will the manager of the chair manufacturing department select if the manager$$s

bonus is based on minimizing the total cost per batch, which includes new and recycled

plastic and plant overhead?

c$.$ Why are your answers to parts $($a$)$ and $($b$)$ either the same or different?

d$.$ Should the plastic chairs manufacturing manager$$s bonus be based on minimizing only

the plastic costs or should it also be based on minimizing plastic costs plus allocated plant

overhead?