A manufacturer produces a 4-cup and 8-cup coffee maker. The 4-cup maker takes 6 hours to produce and the 8-cup takes 9 hours. The manufacturer has at most 500 hours of labor per week.
a. Write an inequality to represent the number of each type of coffee makers they can produce in a week.
b. Is it possible to produce 20 4-cup and 30 8-cup coffee makers in a given week? Explain why or why not showing all of your calculations.
6 f + 9 e </= 500
6 (20) + 9 (30) = 390 hours, sure that is less than 500 hours
a. In order to write an inequality to represent the number of each type of coffee makers they can produce in a week, let's assume x represents the number of 4-cup coffee makers they can produce and y represents the number of 8-cup coffee makers they can produce.
We know that the 4-cup coffee maker takes 6 hours to produce, and the 8-cup coffee maker takes 9 hours to produce. So, the total labor hours used to produce x 4-cup coffee makers would be 6x, and the total labor hours used to produce y 8-cup coffee makers would be 9y.
We also know that the manufacturer has at most 500 hours of labor per week. So, the inequality representing the number of each type of coffee makers they can produce in a week would be:
6x + 9y ≤ 500
b. To determine whether it is possible to produce 20 4-cup and 30 8-cup coffee makers in a given week, we need to substitute the values of x and y into the inequality and check if it is satisfied.
Substituting x = 20 and y = 30 into the inequality:
6(20) + 9(30) ≤ 500
120 + 270 ≤ 500
390 ≤ 500
Since 390 is less than or equal to 500, the inequality is satisfied. Therefore, it is possible to produce 20 4-cup and 30 8-cup coffee makers in a given week, given the labor constraints.