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83% (01:59) correct
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\(5p + 3q ≤ 17,000\)
\(7p + 9q ≤ 43,000\)
A manufacturer wants to make p screws and q nails from a shipment of raw material. Material constraints require p and q to satisfy the inequalities given above. What is the maximum total number of screws and nails that can be created, given the material constraints?\(7p + 9q ≤ 43,000\)
(A) 4,000
(B) 5,000
(C) 6,000
(D) 7,000
(E) 8,000
13 Feb 2024, 01:12
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Check out question 3 in the video below for the solution:
21 Mar 2025, 23:13
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\(5p + 3q ≤ 17,000\) (eq 1)
\(7p + 9q ≤ 43,000\) (eq 2)
\(12p + 12q ≤ 60,000\) (eq 1+ eq2)
\(p + q ≤ 5,000\) (eq 3)
Answer is 5000
Extra work
\(2p ≤ 2,000\) (eq 1+ eq3)
\(p ≤ 1,000\) (eq 4)
\(2q ≤ 8,000\) (eq 2+ eq 3)
\(q ≤ 4,000\) (eq 5)
\(p + q ≤ 5,000\) (eq 4 + eq 5)
\(7p + 9q ≤ 43,000\) (eq 2)
\(12p + 12q ≤ 60,000\) (eq 1+ eq2)
\(p + q ≤ 5,000\) (eq 3)
Answer is 5000
Extra work
\(2p ≤ 2,000\) (eq 1+ eq3)
\(p ≤ 1,000\) (eq 4)
\(2q ≤ 8,000\) (eq 2+ eq 3)
\(q ≤ 4,000\) (eq 5)
\(p + q ≤ 5,000\) (eq 4 + eq 5)
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