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The table below shows Crystal’s total cost of producing different quantities of tie-dyed t-shirts for a local arts festival.  Instructions: Enter your answers as a whole number. a. Complete the marginal cost column in the table. Tie-Dyed T-Shirt Production CostsOutput Total Cost (dollars) Marginal Cost (dollars)0 $15 —1 18 $ 2 20 3 21 4 24 5 29 6 36  b. Graph the marginal cost curve for producing tie-dyed t-shirts. Instructions: Use the tool provided “Marginal Cost” to plot the line point by point (6 points total). Plot from 1 to 6 units of output.  c. What is the total cost of producing 5 tie-dyed t-shirts?     $   d. What is the marginal cost of producing the 5th tie-dyed t-shirt?      $

Question

The table below shows Crystal’s total cost of producing different quantities of tie-dyed t-shirts for a local arts festival.  Instructions: Enter your answers as a whole number. a. Complete the marginal cost column in the table. Tie-Dyed T-Shirt Production CostsOutput Total Cost (dollars) Marginal Cost (dollars)0 1511815 —1 18 2 20 3 21 4 24 5 29 6 36  b. Graph the marginal cost curve for producing tie-dyed t-shirts. Instructions: Use the tool provided “Marginal Cost” to plot the line point by point (6 points total). Plot from 1 to 6 units of output.  c. What is the total cost of producing 5 tie-dyed t-shirts?       d.Whatisthemarginalcostofproducingthe 5thtiedyedtshirt?        d. What is the marginal cost of producing the 5th tie-dyed t-shirt?     

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Solution

a. The marginal cost is the cost of producing one additional unit. It can be calculated by subtracting the total cost of producing the previous unit from the total cost of producing the current unit. Here's how you calculate it for each unit:

  • For the first t-shirt, the marginal cost is 1818 - 15 = $3.
  • For the second t-shirt, the marginal cost is 2020 - 18 = $2.
  • For the third t-shirt, the marginal cost is 2121 - 20 = $1.
  • For the fourth t-shirt, the marginal cost is 2424 - 21 = $3.
  • For the fifth t-shirt, the marginal cost is 2929 - 24 = $5.
  • For the sixth t-shirt, the marginal cost is 3636 - 29 = $7.

So, the completed table is:

Tie-Dyed T-Shirt Production Costs Output Total Cost (dollars) Marginal Cost (dollars) 0 15115 — 1 18 323 2 20 232 3 21 141 4 24 353 5 29 565 6 36 $7

b. To graph the marginal cost curve, plot the number of units produced on the x-axis and the marginal cost on the y-axis. Then, plot a point for each unit of output at its corresponding marginal cost. Connect the points with a line to form the curve.

c. The total cost of producing 5 tie-dyed t-shirts is $29.

d. The marginal cost of producing the 5th tie-dyed t-shirt is $5.

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