Pepsi Cost Analysis

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That means for the radius of 3.35, h = 355 / πr² h = 355 / π(3.35)² h = 10.07 cm. The cost of making the narrower can by Pepsi costs 658.84 rupees while the wider can cost 635.72 rupees. Therefore making these the dimensions of a can, which would have the least cost production of aluminum. The optimum can has a total cost of 635.41, making it 0.31 rupees cheaper than the wider Pepsi can which costs 635.72 rupees. Hence the most cost saving dimensions are 10.07 height and 3.35 cm radius. Step 5: Checking that the minimum cost value was correct using differential calculus. From the formula, we can see that the total cost of the can is a function consisting of only one variable (r). Total cost of making the can: 6πr² + …show more content…

The narrower can costs 658.84 rupees while the wider can cost 635.72 rupees. There is hence, a significant difference in cost between the narrower and wider …show more content…

But, even thought this had the least total surface area of a can of 355 ml, it wasn't the cheapest, due to different prices for the top and bottom area and a cheaper aluminum cost for the curved surface area. (277.9 + 369.6 = 647.5 rupees). Hence, I created the formula that could be used for an unknown variable radius ‘r’ in relation to the total cost of the can = 6πr² + 4πr (355 / πr²). After plotting this value on a graph, I saw that the minimum value of the radius was 3.35 and the height being 10.07 cm. This gave the cheapest cost of producing the can with aluminum. Also then, I wanted to double check if this method was correct, so I checked it using differential calculus and got the same result. Therefore, I can conclude that the minimum cost value (635.41) is in agreement with both methods, the differential calculus one and by plotting a graph of the total cost and finding the minimum value. To conclude, I would like to state my investigation is not thoroughly accurate and this could be because I did not take into consideration the factor that the Pepsi can is not an exact cylinder, as it has a light dome like structure joining the top and bottom. = 369.6

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