A food-processing company gradually closes down the production of potato chips w

Question

A food-processing company gradually closes down the production of potato chips when the strawberry season begins. If the quantity of chips produced is 10500 bags per week and reduction is at the rate of 20% each week and 200 KG of strawberries is processed in the first week of the season, increasing by 100 kg each for eight weeks, calculate:

a) The number of bags of chips and kg of strawberries produced in week 5 of the strawberry season

b) The number of weeks taken for the production of chips to drop to 500 bags per week

c) The total weight of strawberries processed in eight weeks

Explanation / Answer

(a) As number of potato chips bags production is reducing at the rate of 20% per week.

therefore, Number of bags produced in week 5 = 10500 * (1 - 0.2)^5 = 3440.64 = 3441 bags

Strawberries processed in week 5 = 200 + 100*4 = 600 Kgs.

(b) Let n be the number of weeks required for the production of 500 bags potato chips

500 = 10500 * (0.8)^n

0.0476 = (0.8)^n

Take log on both side,

Log (0.0476) = n Log(0.8)

n = Log (0.0476) / Log (0.8)

n = 13.64

This means it will take 14 weeks to decrease the potato chips production to 500 bags per week.

(c) Total weight of strawberries processed in 8 Weeks = 200 + 300 + 400 + 500 + 600 + 700 + 800 + 900 = 4400 Kgs.

Below is the consolidated table,

Week # Potato Chips (bags) Strawberry (Kg) 0 10500 0 1 8400 200 2 6720 300 3 5376 400 4 4301 500 5 3441 600 6 2753 700 7 2202 800 8 1762 900 4400 9 1409 1000 10 1127 1100 11 902 1200 12 722 1300 13 577 1400 14 462 1500

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