Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you mame a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and you need to make at least $3850 profit on them. How many of what type of printer should you order if you want to minimize your cost?

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Mathematics

10 April, 05:16

Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you mame a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and you need to make at least $3850 profit on them. How many of what type of printer should you order if you want to minimize your cost?

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Troy Welch · Answer 1

Let x represent the number of A printers

Let y represent the number of B printers

Minimize cost = 86x + 130y

subject to

Total printers equn: x + y ≥ 100

Total profit equn: 45x + 35y ≥ 3850

x ≥ 0, y ≥ 0

x and y must be whole numbers.

The vertices of the feasible region are: (0, 100), (100, 0) and (35, 65)

If x = 35 and y = 65 the cost is 11460 and profit is 3850

if x = 100 and y = 0 the cost is 8600 and profit is 4500

If x = 0 and y = 100 the cost is 13000 and profit is 3500

The best result is x = 100 and y = 0