A clothing design company pays two different people to design its t-shirts. The company pays pets A $15 an hour and pays person B $18. Person A cannot work more than 5 more hours than person B, but they cannot work more than 30 hours total. Person A makes the company a profit of $20 an hour and person B makes the company a profit of $25 an hour. If the company wants to make at least $300 in profit, what value will minimize the cost to the company?
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In this question we will form inequalities.
Let time taken by B be X hrs and B will be (X - 5) hrs
According to the question :
X + X - 5 < 30
Solving for x
2X < 35
X < 17.5 hrs........ 1
The profit made by A and B respectively are :
20 and 25
The total profit intended to be made by the company should be
Profit ≥ 300
Given that A works for (x - 5) hrs and B works for x hrs then :
Total profit to be made is :
20(x - 5) + 25 (x) ≥ 300
20x - 100 + 25x ≥ 300
45x ≥ 300 +100
45x ≥ 400
x ≥ 8. 9
The inequality that minimizes the cost is thus :
8.9 ≤ x < 17.5
Let time taken by B be X hrs and B will be (X - 5) hrs
According to the question :
X + X - 5 < 30
Solving for x
2X < 35
X < 17.5 hrs........ 1
The profit made by A and B respectively are :
20 and 25
The total profit intended to be made by the company should be
Profit ≥ 300
Given that A works for (x - 5) hrs and B works for x hrs then :
Total profit to be made is :
20(x - 5) + 25 (x) ≥ 300
20x - 100 + 25x ≥ 300
45x ≥ 300 +100
45x ≥ 400
x ≥ 8. 9
The inequality that minimizes the cost is thus :
8.9 ≤ x < 17.5
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