# Math Problem. Have tried on my own. If you can help please provide a detailed explanation of how you got the answer.Engineering estimates indicate that the variable cost of manufacturing a new...

Math Problem. Have tried on my own. If you can help please provide a detailed explanation of how you got the answer.

Engineering estimates indicate that the variable cost of manufacturing a new product will be $35 per unit. Based on market research, the selling price of the product is to be $72 per unit and there is an additional selling expense which is estimated to cost the company $10 per unit. The fixed costs applicable to this new product are budgeted at $4,800 per period and the initial production capacity is 430 units. Given this information determine the following:

The sales volume in dollars that would result in a loss of no more than $1,020.

The breakeven point in units if the fixed costs are increased to $5,315.

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The variable cost of manufacturing a new product will be $35 per unit. There is also an additional selling expense of $10 per unit. The fixed costs for manufacturing the product are $4800 which would allow the production of 430 units.

The price at which the product is sold is $72 per unit.

If x units of the product are produced, the cost incurred is $4300 + 45*x. The sales revenue is $72*x

For a loss of $1020, $4800 + 45*x - $72*x = 1020

=> -27x = -3780

=> x = 140**The sales volume if 140 units are produced is $10080. The sales volume has to be greater than $10080 if the loss has to be less than $1020.**

Let the break-even point in units if fixed costs are $5315 be x

5315 + 45x = 72x

=> 27x = 5315

=> x = 197 units

**Break-even is achieved when 197 units are produced.**

x = number of units sold

35x = a manufacturing cost

10x = sales expense

fixed cost = 4800

72x = income from sales

sales - fixed cost - variable cost > -1020

72x - 4800 - 35x - 10x > -1020

27x > 3780

x > 140

For the break even point with fixed costs at 5315

72x - 5315 - 35x - 10x > 0

27x > 5315

x > 197

To lose $1020 or less per period the sales must be at least than 140 units. To break even with fixed costs at $5315, the sales must be at least 197 units.