Question 84074
Cost of producing the medals is:{{{C = 12x+39}}}
The revenue (income) from selling the medals is: {{{R = 25x}}} Both amounts in dollars.
1) The break-even quantity is found when the the revenue equals the cost, so setting R = C.
{{{25x = 12x+39}}} Subtract 12x from both sides.
{{{13x = 39}}} Divide both sides by 13.
{{{x = 3}}} The break-even quantity, which is just what you had.
2) To find the profit P, you subtract the cost from the revenue.
{{{P = R-C}}}
{{{P = 25x-(12x+39)}}} Simplify this.
{{{P = 25x-12x-39}}}
{{{P = 13x-39}}} For 250 units, x = 250
{{{P = 13(250)-39}}}
{{{P = 3250-39}}}
{{{P = 3211}}} Profit on 250 units is $3,211.00
Notice that your answer was a negative quantity and this would indicate a loss.
3) The number of units sold to make a profit of $130.00 is found by:
{{{P = 13x-39}}} Substitute P = 130 and solve for x.
{{{130 = 13x-39}}} Add 39 to both sides.
{{{169 = 13x}}} Divide both sides by 13.
{{{13 = x}}} You would need to sell 13 units to make a profit of $130.00
4) Remember: {{{F = (9/5)C+32}}} Substitute C = 30.
{{{F = (9/5)(30)+32}}}
{{{F = 54+32}}}
{{{F = 86}}}