2. A manufacturing firm which manufactures office furniture finds that it has the following variable costs in dollars.
Desks Chairs Tables Cabinets
[50 20 15 25]
[30 15 12 15]
[30 15 8 20]
Assume that an order of 5 desks, 6 chairs, 4 tables and 12 cabinets has just been received. What are the total material, labor and overhead costs associated with the production of ordered items?
3. Asrat Carpet Company has in inventory 1,500 square yards of wool and 1,800 square yards of nylon for the manufacture of carpeting. Two grades of carpeting are produced. Each roll of superior grade carpeting requires 20 sq. yards of wool and 40 square yards of nylon. Each roll of quality-grade carpeting requires 30 square yards of wool and 30 square yard of nylon. If Asrat would like to use all the material in inventory, how many rolls of superior and how many rolls of quality carpeting should be manufactured?
2. To calculate the total material, labor and overhead costs associated with the production of ordered items, we need to multiply the quantity of each item by their respective variable costs and then sum them up.
Quantity of desks: 5
Quantity of chairs: 6
Quantity of tables: 4
Quantity of cabinets: 12
Variable costs (in dollars):
Desks: $50
Chairs: $20
Tables: $15
Cabinets: $25
Total material cost for desks: 5 * $50 = $250
Total material cost for chairs: 6 * $20 = $120
Total material cost for tables: 4 * $15 = $60
Total material cost for cabinets: 12 * $25 = $300
Total material cost: $250 + $120 + $60 + $300 = $730
Labor and overhead costs are not given, so we cannot calculate them based on the information provided.
3. To use all the material in inventory, we can set up a system of equations to represent the requirements for each grade of carpeting:
Let's assume the number of rolls of superior grade carpeting is X, and the number of rolls of quality grade carpeting is Y.
The requirements for superior grade carpeting are:
20X sq. yards of wool
40X sq. yards of nylon
The requirements for quality grade carpeting are:
30Y sq. yards of wool
30Y sq. yards of nylon
Given that there are 1500 sq. yards of wool and 1800 sq. yards of nylon, the equations can be set up as follows:
20X + 30Y = 1500
40X + 30Y = 1800
To solve this system of equations, we can use the elimination method.
Multiplying the first equation by 4 to make the coefficients of X in both equations the same:
80X + 120Y = 6000 (equation 1)
40X + 30Y = 1800 (equation 2)
Subtracting equation 2 from equation 1 to eliminate X:
40X + 90Y = 4200
Subtracting this new equation from equation 2 to eliminate Y:
-60Y = -2400
Y = 40
Substituting the value of Y back into equation 2 to find X:
40X + 30(40) = 1800
40X + 1200 = 1800
40X = 600
X = 15
Therefore, 15 rolls of superior grade carpeting and 40 rolls of quality grade carpeting should be manufactured to use all the material in inventory.