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. $\begin{array}{|c|c|c|c|c|c|}
\hline \text { Process } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\text { (smoke/day) } & \text { (4 tons/day) } & \text { (3 tons/day) } & \text { (2 tons/day) } & (1 \text { ton/day) } & \text { (0 tons/day) } \
\hline \text { Cost to Firm } X(\$ / \text { day) } & \$ 500 & \$ 514 & \$ 530 & \$ 555 & \$ 585 \
\hline \text { Cost to Firm Y (\$/day) } & \$ 400 & \$ 420 & \$ 445 & \$ 480 & \$ 520 \
\hline \text { Cost to Firm Z(\$/day) } & \$ 300 & \$ 325 & \$ 360 & \$ 400 & \$ 550 \
\hline
\end{array}$
Suppose the government imposes a tax of $21 on each ton of smoke emitted. To minimize costs, Firm X will emit ______ tons; Firm Y will emit ______ tons, and Firm Z will emit ______ tons.
A)1; 2; 3
B)2; 3; 4
C)3; 4; 4
D)1; 2; 4

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. $\begin{array}{|c|c|c|c|c|c|}
\hline \text { Process } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\text { (smoke/day) } & \text { (4 tons/day) } & \text { (3 tons/day) } & \text { (2 tons/day) } & (1 \text { ton/day) } & \text { (0 tons/day) } \
\hline \text { Cost to Firm } X(\$ / \text { day) } & \$ 500 & \$ 514 & \$ 530 & \$ 555 & \$ 585 \
\hline \text { Cost to Firm Y (\$/day) } & \$ 400 & \$ 420 & \$ 445 & \$ 480 & \$ 520 \
\hline \text { Cost to Firm Z(\$/day) } & \$ 300 & \$ 325 & \$ 360 & \$ 400 & \$ 550 \
\hline
\end{array}$
 Suppose the government imposes a tax of $21 on each ton of smoke emitted. To minimize costs, Firm X will emit ______ tons; Firm Y will emit ______ tons, and Firm Z will emit ______ tons.
A)1; 2; 3
B)2; 3; 4
C)3; 4; 4
D)1; 2; 4

Quizplus · Accepted Answer

To minimize costs, each firm should choose the processes with the lowest cost per unit of smoke emitted. After the tax, the cost per unit of smoke emitted is the original cost plus the tax per unit, which is $\$ 555+(\$21/	ext{ton})=\$ 576$ for Firm X, $\$ 480 + (\$ 21 / 	ext{ton}) = \$ 501$ for Firm Y, and $\$ 400 + (\$21/	ext{ton})=\$ 421$ for Firm Z.

For Firm X, the lowest cost per unit of smoke is for process D, which emits 1 ton of smoke per day. For Firm Y, the lowest cost per unit of smoke is for process C, which emits 2 tons of smoke per day. For Firm Z, the lowest cost per unit of smoke is for process B or C, both of which emit 3 tons of smoke per day. Choosing process C for Firm Z will result in the lowest total cost, so Firm Z should emit 3 tons/day of smoke. Therefore, the final answer is (B)

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