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.
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.