Suppose there are three power-generating plants, each of which has access to 5 different production processes. The table below summarizes the cost of each production process and the corresponding number of tons of smoke emitted each. $\begin{array}{|c|c|c|c|c|c|}
\hline \text { Process } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\text { (smoke/day) } & \text { (4 tons/day) } & \text { (3 tons/day) } & \text { (2 tons/day) } & (1 \text { ton/day) } & \text { (0 tons/day) } \
\hline \text { Cost to Firm } X(\$ / \text { day) } & \$ 500 & \$ 514 & \$ 530 & \$ 555 & \$ 585 \
\hline \text { Cost to Firm Y (\$/day) } & \$ 400 & \$ 420 & \$ 445 & \$ 480 & \$ 520 \
\hline \text { Cost to Firm Z(\$/day) } & \$ 300 & \$ 325 & \$ 360 & \$ 400 & \$ 550 \
\hline
\end{array}$
The least costly way of lowering smoke emissions from 12 tons to 9 tons per day would be for:
A)each firm to reduce emissions by 1 ton, emitting 3 tons each.
B)Firm X to emit 2 tons, Firm Y to emit 3 tons and Firm Z to emit 4 tons.
C)Firm X to emit 4 tons, Firm Y to emit 3 tons and Firm Z to emit 2 tons.
D)Firm X to emit 1 ton, Firm Y to emit 4 tons and Firm Z to emit 4 tons.

Question

Suppose there are three power-generating plants, each of which has access to 5 different production processes. The table below summarizes the cost of each production process and the corresponding number of tons of smoke emitted each. $\begin{array}{|c|c|c|c|c|c|}
\hline \text { Process } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\text { (smoke/day) } & \text { (4 tons/day) } & \text { (3 tons/day) } & \text { (2 tons/day) } & (1 \text { ton/day) } & \text { (0 tons/day) } \
\hline \text { Cost to Firm } X(\$ / \text { day) } & \$ 500 & \$ 514 & \$ 530 & \$ 555 & \$ 585 \
\hline \text { Cost to Firm Y (\$/day) } & \$ 400 & \$ 420 & \$ 445 & \$ 480 & \$ 520 \
\hline \text { Cost to Firm Z(\$/day) } & \$ 300 & \$ 325 & \$ 360 & \$ 400 & \$ 550 \
\hline
\end{array}$
 The least costly way of lowering smoke emissions from 12 tons to 9 tons per day would be for:
A)each firm to reduce emissions by 1 ton, emitting 3 tons each.
B)Firm X to emit 2 tons, Firm Y to emit 3 tons and Firm Z to emit 4 tons.
C)Firm X to emit 4 tons, Firm Y to emit 3 tons and Firm Z to emit 2 tons.
D)Firm X to emit 1 ton, Firm Y to emit 4 tons and Firm Z to emit 4 tons.

Quizplus · Accepted Answer

Firm X can reduce emissions by 2 tons by switching from process A to process D, at a cost of $555 - $500 = $55 per day. Firm Y can reduce emissions by 3 tons by switching from process B to process D, at a cost of $480 - $420 = $60 per day. Firm Z can reduce emissions by 4 tons by switching from process C to process D, at a cost of $400 - $360 = $40 per day. The total cost of this reduction is $55 + $60 + $40 = $155 per day, which is less than the cost of any other combination of reductions.

Suppose There Are Three Power-Generating Plants, Each of Which Has