As a graphic artist, nate has just finished producing a new calendar. his calendar cost him $1.00 for the shiny paper, $2.00 for the six color production, and $.25 for the plastic wire that holds it together at the top. the labor in developing the design was 4 hours of work at $50/hour, and labor is being added to the rest of the fixed costs of $400.00. at a price of $12.00 per calendar, how many calendars will nate need to produce and sell in order to break even (cover all his costs, but not make a profit)?

69 calendars. The cost of N calendars is C = F + MN where C = Total cost F = Fixed costs M = Marginal cost per item For this problem, the Fixed costs is the $400.00 given plus the cost of labor at $50 for 4 hours, for an additional $200. Making the total fixed costs being $400 + $200 = $600. The marginal cost are $1.00 + $2.00 + $0.25 = $3.25. So we have: C = $600 + $3.25N Now the money that will be received will be the sale price of the calendar multiplied by the number sold. So P = $12.00N Since we're looking for the break even point, let's set an inequality for these two equations, then solve for N. $600 + $3.25N <= $12.00N $600 <= $8.75N 68.57142857 <= N Since a fractional calendar can't be sold, the artist needs to sell at least 69 calendars to break even.

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