Question

A company has two machines that make widgets. The production costs are listed below. Machine 1: Setup cost $300 and $1.90 per widget Machine 2: Setup cost $500 and $1.40 per widget Find the number of widgets for which the cost to manufacture them on either machine is the same. widgets

Answer 1

the number of widgets for which the cost to manufacture them on either machine is the same is 400 widgets.

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Explanation:

To find the number of widgets for which the cost to manufacture them on either machine is the same, we need to set up an equation where the costs for both machines are equal.

Let x be the number of widgets. The cost to manufacture x widgets on Machine 1 is given by:

Cost on Machine 1 = Setup cost + (Cost per widget) * (Number of widgets)

Cost on Machine 1 = $300 + $1.90x

The cost to manufacture x widgets on Machine 2 is given by:

Cost on Machine 2 = Setup cost + (Cost per widget) * (Number of widgets)

Cost on Machine 2 = $500 + $1.40x

To find the number of widgets for which the cost is the same on both machines, we set the two cost expressions equal to each other and solve for x:

$300 + $1.90x = $500 + $1.40x

Now, let's solve for x:

$0.50x = $200

x = $200 / $0.50

x = 400