A plumber 3

A plumber can buy plastic pipes in 6-foot and 12-foot lengths. The current job requires eight 4-foot lengths, five 5-foot lengths, and three 7-foot lengths. The plumber wants to figure out how many of each of the two stock lengths should be bought to minimize waste.

Final Answer:

a =  4
b =  5

Step-by-step explanation:

$$\begin{gathered} L_1=6\text{ft} \\ {L}_2=12\text{ft} \\ {n}_1=8 \\ {n}_2=5 \\ {n}_3=3 \\ 8\cdot 4ft \\ 5\cdot 5ft \\ 3\cdot 7ft \\ 12=4a+5b+7c \\ {a}_1=0b_1=1c_1=1 \\ {a}_2=3b_2=0c_2=0 \\ 12ft=7+5 \\ 12ft=7+5 \\ 12ft=7+5 \\ 12ft=4+4+4 \\ 12ft=4+4+4 \\ 6ft=5+1 \\ 6ft=5+1 \\ 6ft=4+2 \\ 6ft=4+2 \\ a=4 \\ b=5 \end{gathered}$$

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