High School

PPT Corp manufactures picture frames. Sales for August are expected to be 10,000 units of various sizes. Historically, the average frame requires:

- Four metres of framing
- One square metre of glass
- Two square metres of backing

Beginning inventory includes:

- 1,500 metres of framing
- 500 square metres of glass
- 500 square metres of backing

Current prices are:

- $0.30 per metre of framing
- $6.00 per square metre of glass
- $2.25 per square metre of backing

Ending inventory should be 150% of beginning inventory. Purchases are paid for in the month acquired.

**Required:**

a. Determine the quantity of framing, glass, and backing that is to be purchased during August.

b. Determine the total costs of direct materials for August purchases.

Answer :

To solve this problem, we'll determine the quantity of framing, glass, and backing needed for the production and calculate the total cost of these materials for August. Let's break this down step-by-step:

a. Determine the quantity of materials to be purchased

  1. Calculate the total material needs for August:

    • Framing: Each frame requires 4 metres of framing. So, for 10,000 frames, the total framing needed is:
      [tex]10,000 \times 4 = 40,000 \text{ metres}[/tex]
    • Glass: Each frame needs 1 square metre of glass. Thus, the total glass required is:
      [tex]10,000 \times 1 = 10,000 \text{ square metres}[/tex]
    • Backing: Each frame requires 2 square metres of backing. So, the total backing needed is:
      [tex]10,000 \times 2 = 20,000 \text{ square metres}[/tex]

  2. Calculate the ending inventory requirements:

    • Ending inventory should be 150% of beginning inventory:
      • Framing:
        [tex]150\% \times 1,500 = 2,250 \text{ metres}[/tex]
      • Glass:
        [tex]150\% \times 500 = 750 \text{ square metres}[/tex]
      • Backing:
        [tex]150\% \times 500 = 750 \text{ square metres}[/tex]

  3. Calculate the net purchase requirements:

    • Framing:
      [tex](40,000 + 2,250) - 1,500 = 40,750 \text{ metres}[/tex]
    • Glass:
      [tex](10,000 + 750) - 500 = 10,250 \text{ square metres}[/tex]
    • Backing:
      [tex](20,000 + 750) - 500 = 20,250 \text{ square metres}[/tex]

b. Determine the total costs of direct materials

  1. Calculate the total cost of each material for August purchases:

    • Framing cost:
      [tex]40,750 \times 0.30 = 12,225 \text{ dollars}[/tex]
    • Glass cost:
      [tex]10,250 \times 6.00 = 61,500 \text{ dollars}[/tex]
    • Backing cost:
      [tex]20,250 \times 2.25 = 45,562.5 \text{ dollars}[/tex]

  2. Total cost of all materials:

    • Add all the costs together:
      [tex]12,225 + 61,500 + 45,562.5 = 119,287.5 \text{ dollars}[/tex]

Therefore, the total costs of direct materials for August purchases are $119,287.50.

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