Ralph spent $$5,500$ on a new oven this year in the belief that it would increase his overall gains by $13\%$ over last year. This oven turns "greenware" into finished pottery. Ralph is concerned that the new oven requires extra labor hours for its operation, and wants to check the energy savings of the new oven, and also to look over other measures of their productivity to see if the change really was beneficial. Ralph has the following data to work with:

January $2022$

January $2023$

Production $($finished units$)$

$3,900$

$4,350$

Greenware $($pounds$)$

$3,000$

$4,000$

Labor $($hrs$)$

$380$

$400$

Capital $($$$)$

$$14,500$

$$24,000$

Energy $($kWh$)$

$2,860$

$2,550$

Ralph has other considerations when determining productivity. They are: Greenware averages $$29\mathrm{.}70$ per pound, average labor costs are $$13\mathrm{.}50,$ his average capital invested is $1\%$ per month, and the average cost of energy per BTU is $$0\mathrm{.}75$

Factoring all of the data and the other considerations, answer the following:

a$.$ What was the change in productivity for Greenware

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b$.$ What was the change in productively for Labor

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c$.$ What was the change in productivity for Capital

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d$.$ What was the change in productivity for Energy

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e$.$ Based on multi$-$factor productivity what is last year's ratio

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$,$ and this year's ratio?

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$.$ What was the percent change?

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$,$ and did the new oven achieve its productivity goal?

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