Question

Brenya Estate produces a high quality tea branded A, B and C in the ration 1.5: 5: 1. Originally Type A tea costs 1600, type B costs 800 and type C costs 1700 per kg to produce. Brenya Tea Estate packs Super tea in packets of 825g each. Blending and packing costs are 40 per kg. Determine the production cost for a packet of super tea

Answer 1

Answer:

The production cost for a packet of super tea is 924.

Step-by-step explanation:

The production cost of the Super tea is given as

$Cost_{super\ tea}=Cost_{A}+Cost_{B}+Cost_{C}+Cost_{packaging\ and\ blending}$

Here the costs are given as following

$Cost_A=\dfrac{Ratio\ of\ A}{Sum\ of \ ratios} \times Weight \times Cost\ of\ A\ per\ kg$

Here

• Ratio of A is 1.5
• Sum of Ratios is 1.5+5+1=7.5
• Weight is 825 g or 0.825kg
• Cost of A  per kg is 1600

So

$Cost_A=\dfrac{Ratio\ of\ A}{Sum\ of \ ratios} \times Weight \times Cost\ of\ A\ per\ kg\\Cost_A=\dfrac{1.5}{7.5} \times 0.825 \times 1600\\Cost_A=264$

The cost of A is 264.

Similarly

$Cost_B=\dfrac{Ratio\ of\ B}{Sum\ of \ ratios} \times Weight \times Cost\ of\ B\ per\ kg$

Here

• Ratio of B is 5
• Sum of Ratios is 7.5
• Weight is 825 g or 0.825kg
• Cost of B  per kg is 800

$Cost_B=\dfrac{Ratio\ of\ B}{Sum\ of \ ratios} \times Weight \times Cost\ of\ B\ per\ kg\\Cost_B=\dfrac{5}{7.5} \times 0.825 \times 800\\Cost_B=440$

The cost of B is 440.

Also

$Cost_C=\dfrac{Ratio\ of\ C}{Sum\ of \ ratios} \times Weight \times Cost\ of\ C\ per\ kg$

Here

• Ratio of C is 1
• Sum of Ratios is 7.5
• Weight is 825 g or 0.825kg
• Cost of C  per kg is 1700

$Cost_C=\dfrac{Ratio\ of\ C}{Sum\ of \ ratios} \times Weight \times Cost\ of\ C\ per\ kg\\Cost_C=\dfrac{1}{7.5} \times 0.825 \times 1700\\Cost_C=187$

The cost of C is 187.

Now the packaging and blending cost for the given package is calculated as

$Cost_{packaging\ and\ blending}=Weight*Cost_{packaging\ and\ blending\ per\ kg}$

Here

• Weight is 825 g or 0.825kg
• Cost of packaging and blending  per kg is 40

$Cost_{packaging\ and\ blending}=Weight*Cost_{packaging\ and\ blending\ per\ kg}\\Cost_{packaging\ and\ blending}=0.825*40\\Cost_{packaging\ and\ blending}=33$

Cost of packaging and blending per packet is 33.

So now substituting values of costs in the following equation gives:

$Cost_{super\ tea}=Cost_{A}+Cost_{B}+Cost_{C}+Cost_{packaging\ and\ blending}\\Cost_{super\ tea}=264+440+187+33\\Cost_{super\ tea}=924$

The production cost for a packet of super tea is 924.