Question

A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 6 hours. The company has only 600 work hours to use in manufacturing each day, and the packaging department can package only 200 trimmers per day. If the company's profits are $39.50 for the cord-type model and $118.50 for the cordless model, how many of each type should the company produce per day to maximize profits? Step 1: Let x be the number of cord-type trimmers and y be the number of cordless trimmers. The company can sell each cord-type trimmer for $39.50 and each cordless trimmer for $118.50, so the sales function that we want to maximize is S = 39.50x + 118.50y. The constraints, based on available work hours and packaging limitations, are given by the following: 2x + 6y ≤ 600 x + y ≤ 200 Also note that x ≥ 0 and y ≥ 0 since there can't be a negative number of trimmers.

          A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 6 hours. The company has only 600 work hours to use in manufacturing each day, and the packaging department can package only 200 trimmers per day. If the company's profits are $39.50 for the cord-type model and $118.50 for the cordless model, how many of each type should the company produce per day to maximize profits?

Step 1: Let x be the number of cord-type trimmers and y be the number of cordless trimmers. The company can sell each cord-type trimmer for $39.50 and each cordless trimmer for $118.50, so the sales function that we want to maximize is S = 39.50x + 118.50y. The constraints, based on available work hours and packaging limitations, are given by the following:
2x + 6y ≤ 600
x + y ≤ 200
Also note that x ≥ 0 and y ≥ 0 since there can't be a negative number of trimmers.

Added by Anthony S.

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