a baker bakes bread and cake.he has 150 unit of A ,90 unit of B and 150 of C.
One bread requires 1 unit of A ,1 unit of B and 2 unit of C.
One cake requires 5 units of A, 2 unit of B and 1 unit of C.
Find his maximum income if a bread sells for Tsh.350/= and cake sells for Tsh.500/=
To find the maximum income, we need to determine the maximum number of bread and cake the baker can produce with the given units of A, B, and C.
Let's start with calculating the maximum number of bread the baker can make:
- Units of A: 150
- Units of B: 90
- Units of C: 150
One bread requires:
- 1 unit of A
- 1 unit of B
- 2 units of C
Since the baker can only make as many bread as the least available ingredient can provide, we need to find the limiting factor.
- For the available units of A, the baker can make a maximum of 150 bread (150 units of A ÷ 1 unit of A per bread).
- For the available units of B, the baker can make a maximum of 90 bread (90 units of B ÷ 1 unit of B per bread).
- For the available units of C, the baker can make a maximum of 75 bread (150 units of C ÷ 2 units of C per bread).
Therefore, the baker can only make a maximum of 75 bread based on the availability of ingredient C.
Next, let's calculate the maximum number of cake the baker can make:
- Units of A: 150
- Units of B: 90
- Units of C: 150
One cake requires:
- 5 units of A
- 2 units of B
- 1 unit of C
Again, we find the limiting factor:
- For the available units of A, the baker can make a maximum of 30 cakes (150 units of A ÷ 5 units of A per cake).
- For the available units of B, the baker can make a maximum of 45 cakes (90 units of B ÷ 2 units of B per cake).
- For the available units of C, the baker can make a maximum of 150 cakes (150 units of C ÷ 1 unit of C per cake).
Therefore, the baker can make a maximum of 30 cakes based on the availability of ingredient A.
To calculate the maximum income, we multiply the maximum number of products by their respective selling prices:
- Maximum income from bread: 75 x Tsh.350 = Tsh.26,250
- Maximum income from cake: 30 x Tsh.500 = Tsh.15,000
Therefore, the maximum income the baker can earn is Tsh.26,250 from selling bread and Tsh.15,000 from selling cake.