The financial department ofYG (Pvt.) Ltd. provides the following cost functions regarding the
new product they are planning to manufacture; (cost in Rs) C = 200 + 400Q where Rs. 200 is
the estimated fixed costs and the estimated variable cost is Rs. 400 per unit. The revenue
function (in Rs.) is R = 50Q + 0.05Q2
A. Develop the MC function and calculate MC.
Answers
Answer:
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Question
A manufacturer produces three products x,y,z which he sells in two markets. Annual sales are indicated below:
Market Products
I
10,000 2,000 18,000
II 6,000 20,000 8,000
(a) If unit sale prices of x,y and z are Rs.2.50, Rs.1.50 and Rs.1.00, respectively, find the total revenue in each market with the help of matrix algebra.
(b) If the unit costs of the above three commodities are Rs.2.00,Rs.1.00 and 50 paise respectively. Find the gross profit.
Medium
Solution
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(a) The unit sale prices of x,y and z are respectivelyRs.2.50,Rs.1.50 and Rs.1.00.
Total revenue in market I can be represented as:
[
10000
2000
18000
]
⎣
⎢
⎢
⎡
2.50
1.50
1.00
⎦
⎥
⎥
⎤
=10000×2.50+2000×1.50+18000×1.00
=25000+3000+18000
=46000
Total revenue in market II can be represented as:
[
6000
20000
8000
]
⎣
⎢
⎢
⎡
2.50
1.50
1.00
⎦
⎥
⎥
⎤
=6000×2.50+20000×1.50+8000×1.00
=15000+30000+8000
=53000
So, the total revenue in market I is Rs 46000 and in market II is Rs.53000.
(b) The unit cost prices of x,y and z are respectively given as Rs.2.00, Rs.1.00 and 50 paise.
So, the total cost prices of all the products in market I can be represented as:
[
10000
2000
18000
]
⎣
⎢
⎢
⎡
2.00
1.00
0.50
⎦
⎥
⎥
⎤
=10000×2.00+2000×1.00+18000×0.50
=20000+2000+9000
=31000
Since, the total revenue in market I is Rs.46000.
So, the gross profit in this market is Rs46000−Rs31000=Rs15000.
The total cost prices of all the products in market II can be represented as:
[
6000
20000
8000
]
⎣
⎢
⎢
⎡
2.00
1.00
0.50
⎦
⎥
⎥
⎤
=6000×2.00+20000×1.00+8000×0.50
=12000+20000+4000
=Rs36000
Since, the total revenue in market II is Rs.53000.
So, the gross profit in this market is Rs.53000−Rs.36000=Rs.17000.