If anyone could help me with these questions it would be greatly appreciated. Also if you could provide a step by step of how you got the answers that would be great!

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:

a) The income at a sales volume of 70 units.
b) The profit or loss at a volume of 30% of capacity.
c) The net income assuming total sales of $23,400.
d) The number of units that must be sold to achieve a net income of at least $5,000.

a) We sold 70 Units, so 70 * 72$(Sale Prize) = 5040$ So our income for 70 Units is 5040$

b) 30% of 430 Max Capacity = 430 / 100 *30 = 129 Units

First we get our income (like "a"): 129 * 72$(Sale Prize) = 9288$

Second we need our production costs for 129 Units: $35 + 10$ = "45$ production costs per unit"

129 * 45$ = 5805$ Production costs for 129 Units

Next Fixed Costs for the whole Production + Production Costs for 129 Units

4800$ + 5802$ = 10605$

So the profit / loss for selling and production of 129 Unit (30%) is = 9288$ Income - 10605$ Production Costs

= -1317$ Loss


C) Net Income assuming total sales of $23,400

First Income divided with sale prize for one unit

23400$ / 72$ = 325 Units

This means we sold 325 Units to get an income of 23400$ now we need the NET Income for 325 Units:

325 * 45$ (production costs per unit) = 14625$ + Fixed Costs 4800$ = 19425$ Costs for the Whole Production

So the Net Income is: 23400$ - 19425$ = 3975$ NET INCOME


d) we need to achieve a Net Income of 5000$

First we need the net income for one unit without the fixed costs:

72$(sale prize) - 45$(production costs per unit) = 27$

Now we can say :

x*27 - 4800 = 5000 |+4800
x*27 = 9800 | /27
x = 362,96... ~ 363 Units

So we need at least 363 Units to achieve a Net Income of 5000$, because: 363 Units * 27$ (72$-45$) = 9801$ - Fixed Costs(4800$) = 5001$ Net Income!!