Question

A company makes two products in a single plant. It runs this plant for 100 hours each week. Each unit of product A that the company produces consumes two hours of plant capacity, earns the company a contribution of $1000, and causes, as undesirable side effects, the emission of 4 ounces of particulates. Each unit of product B that the company produces consumes one hour of capacity earns the company a contribution of $2000, and causes, as undesirable side effects, the emission of 3 ounces of particulates and 1 ounce of chemicals. The EPA (Environmental Protection Agency) requires the company to limit the particulate emission to at most 240 ounces per week and chemical emission to at most 60 ounces per week.

The EPA wants to reduce the release of chemicals into the atmosphere by imposing a fine of $1000 per ounce. Would the government's fine be effective at curbing the release of chemicals?

True or False

Answer 1

Facts

Plant Capacity for a week = 100 hours

Each unit of Product A consumes two hours of plant capacity and earns a contribution of $1,000 and emits 4 ounces of particulates

Each unit of Product B consumes one hour of plant capacity and earns a contribution of $2,000 and emits 3 ounces of particulates and 1 ounce of chemical.

Particulate emission allowed per week = 240 ounces and chemical emission allowed is 60 ounces.

Ranking the products

Product	A	B
Hours required per unit	2	1
Contribution	1,000	2,000
Contribution per hour	500	2,000
Rank	II	I

Production per week

Product	Units	Hours	Cumulative hours
B	60	60	60
A	15	30	90

Note - Product B gives the highest contribution per unit of plant hours (bottleneck) hence it is to be produced in the highest quantity. Only 60 ounces of chemical emission is allowed per week, each unit of product B emits one unit of chemical hence only 60 units of Product B can be produced.

Product A emits 4 ounces of particulates and only 240 ounces of particulates emission is permitted out of which already 180 ounces are emitted during production of 60 units of product B. The emission allowable for product A is only 60 ounces of particulates and each unit of Product A emits 4 ounces of particulates, hence only 15 units of Product A can be produced.

Only 90 hours out of 100 hours of plant capacity is being used.

Contribution per week based on the above production

Product	Units	Contribution per unit	Contribution
B	60	2,000	120,000
A	40	1,000	40,000
			160,000

Effect of Fine

Fines if any imposed by the EPA would surely reduce the emission but also would be met by heavy criticism. Due to the existing regulations for emission there is already an unused capacity of 10 plant hours (100-90) per week. Further fines would affect the contribution from production of product B (the most profitable product) since production of B alone emits chemicals.

It is assumed that EPA wants to reduce the chemical emission from 60 ounces to zero ounces and would impose fine of $1,000 per ounce of chemical, this would impair the ability of the company to produce product B. The contribution of company would fall to $ 60,000 (from production of 60 units of product A that emits 240 units of particulates).Hence EPA has to also consider the economic consideration before imposing any fines.

Any company would shy away from activities that leads to imposition of fines to show themselves as socially responsible.This company would also do the same and not produce the product that leads to emission of chemicals.