The profit made by a company when 60 units of its product is sold is R1600.00. When 150 units of its product is sold, the profit increases to R5200. Assuming that the profit function is linear and of the form
P(u) =a+but where Possible is the profit in Rands and u is the number of units sold, determine the:
1. Value of a and b
2. Break-even level
3. Number of units that need to be sold to realise a profit of R12 000. 00
Answers
Answer:
1. a = -800 and b = 40
2. If you produce and sell 20 units, break even is reached.
3. You need to sell 320 units to get a profit of Rs. 12000.
Step-by-step explanation:
Profit equation is given by
P(u) = a + bu
Number of Units made = u = 60
Profit = Rs. 1600
Hence equation is 1600 = a + 60b ----------------------------E1
Number of units made = 150
Profit = Rs. 5200
Hence equation is 5200 = a + 150b ------------------------------E2
E2 – E1 gives us
3600 = 90b
b = 40
Hence a = 1600 – 60 * 40 = -800.
1. a = -800 and b = 40
break even is when the profit exactly zero.
0 = -800 + 40u
u = 800/40 = 20.
2. If you produce and sell 20 units, break even is reached.
3. Profit = Rs. 12000
12000 = -800 + 40u
Hence u = (12000 + 800)/40 = 12800/40 = 320
You need to sell 320 units to get a profit of Rs. 12000.
Answer:
a = -800
b = 40
20 units for break even
320 units for Rs 12000 profit
Step-by-step explanation:
The profit made by a company when 60 units of its product is sold is R1600.00. When 150 units of its product is sold, the profit increases to R5200. Assuming that the profit function is linear and of the form
P(u) =a+but where Possible is the profit in Rands and u is the number of units sold, determine the:
1. Value of a and b
2. Break-even level
3. Number of units that need to be sold to realise a profit of R12 000. 00
P(u) = a + bu
P(60) = 1600
1600 = a + 60b
P(150) = 5200
5200 = a + 150b
=> 90b = 3600
=> b = 40
1600 = a + 60(40)
=> a = -800
P(u) = -800 + 40u
Break even when profit = 0
0 = -800 + 40u
u = 20
20 units
12000 = -800 + 40u
=> u = 12800/40
=> u = 320