Melissa Bright Jewelry, Inc. is a jewelry manufacturer. It has a factory located in Hartford, CT$.$ It imports raw materials and hires skilled labor to assemble the finished products. The manufacturing process involves metal welding which uses lots of electricity. The average sales price per unit of finished product is $$50.$

Melissa Bright Jewelry$$s raw materials are purchased in ounces. The per ounce purchase price is $$3\mathrm{.}80.$

Melissa Bright Jewelry, Inc. pays $$16$ per hour to its labor on the production line. In addition, it is required to pay the employment taxes at $7\mathrm{.}65\%$ of the wages and other benefits at $24\%$ of wages. It takes $15$ minutes $($including break time$)$ on average for one manufacturing labor to finish one piece of product.

Other expenses include rent, insurance, and managerial salaries. The amount of these expenses are stable every month.

The costs of supplies vary by production unit. The average cost per unit is $$0\mathrm{.}70.$

Utility expenses and the production units in the past $12$ months are summarized in the table in the Excel file. The manager understands that the more units produced, the higher the electricity bill. But she does not know what the per$-$unit electricity cost is$.$

The regression method:

$$ You may use the Data Analysis to run the full regression statistics $($see Video$),$ or simply use the following formula in excel:

o $=$slope$($Y series, X series$)$: this function returns the beta, or the variable cost per unit

o $=$intercept$($Y series, X series$)$: this function returns the intercept, or the fixed cost

o Select the data range of the charges as Y series. Select the production quantity as the X series.

Please answer the following questions:

$1)$What is the cost of direct materials per unit?$[$Please round your answer to three decimal places.$]$

$2)$What is the cost of direct labor per unit? $[$Please round your answer to three decimal places.$]$

$3)$What is the variable manufacturing overhead cost per unit?

For mixed costs $($part fixed and part variable$),$ you will need to determine what is the fixed portion and what is the variable portion of the cost. Please use either the Data Analysis to run the full regression statistics $($see Video$),$ or the following formula in excel to determine the fixed portion and the variable portion $($per unit$)$o $=$slope$($Y series, X series$)$: this function returns the beta, or the variable cost per unit

o $=$intercept$($Y series, X series$)$: this function returns the intercept, or the fixed cost

o Select the data range of the charges as Y series. Select the production quantity as the X series.

$[$Please round your answer to three decimal places.$]$

$4)$What is the contribution margin per unit?

$[$Please round your answer to three decimal places.

$5)$What is the cost of the fixed portion of the utility cost?

For mixed costs $($part fixed and part variable$),$ you will need to determine what is the fixed portion and what is the variable portion of the cost. Please use either the Data Analysis to run the full regression statistics $($see Video$),$ or the following formula in excel to determine the fixed portion and the variable portion:

o $=$slope$($Y series, X series$)$: this function returns the beta, or the variable cost per unit

o $=$intercept$($Y series, X series$)$: this function returns the intercept, or the fixed cost

o Select the data range of the charges as Y series. Select the production quantity as the X series.

$[$Please round your answer to a whole number.$]$

$6)$What is the total fixed manufacturing overhead cost?

$[$Please round your answer to a whole number.$]$

$7)$What is the break$-$even unit?

$[$Please round your answer to a whole number.$]$

$8)$If Melissa Bright Jewelry would like to have a monthly profit of $$75,000,$ how many units should Melissa Bright Jewelry sell each month?

$[$Please round your answer to a whole number.$]$

$9)$If Melissa Bright Jewelry can only sell $3,000$ units per month and still wants to have $$75,000$ profit per month, how much Melissa Bright Jewelry should sell for each unit? $($Assume that the unit of sales will NOT be affected by the price increase$).$