MAT1106: A company makes (window) frames and doors. It makes a profit of $30 on frames and $35 on a door: Business Mathematics Assignment, IIU, Malaysia

Question 1

A company makes (window) frames and doors. It makes a profit of $30 on frames and $35 on a door.
Each frame requires 5 units of materials, 3 units of machine time and 2 units of labour. Each door requires 8 units of material, 5 units of machine time and 1 unit of labour. The resources available are 400 units of materials, 500 units of machine time and 100 units of labour.

• Formulate this as a linear programming problem listing the constraints and
  objective function.
• Graph the linear inequalities and shade the feasible region.
• How many of each type should be produced to maximize the profit?
• What is the maximum profit?

Question 2

Draw each inequality and shade the feasible region

Question 3

Mac Electronic Company manufactures and sells headphone set. After suitable test marketing, the research department presents the following price-demand equation:

𝑝(𝑥) = 900 − 5𝑥, where x is the number of headphones and p is the unit price.

The financial department estimated $2000 for fixed costs. The variable cost is $300 per headphone set.

• Find the revenue function and cost function.
• Find the marginal revenue and its value when x = 20.
• Find the profit function.
• Determine the output level to maximize the profit and find the maximum profit.
• Find the marginal profit function.

Question 4

A profit function is given by

• Calculate the break-even points. Show a graphical representation for the
  points.
• What is your decision on the quantity to produce and sell to break even?

Answer

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