a furniture company has been designing a coffee table made of bamboo for several months. the design costs…

a furniture company has been designing a coffee table made of bamboo for several months. the design costs will be approximately $5850. each table will cost $90 for material and labor. the company has decided to sell each table for 220 dollars.\ndefine units for the cost of production and the income obtained from the tables. enter a variable for the number of tables produced and use this variable to write expressions for the cost of production and the income obtained from the tables.\n1. what is the initial cost of production? what is the initial income?\n2. how much will the cost be and how much income would be obtained if 190 tables are produced?\n3. if the income was $39,600, how many tables were sold?

a furniture company has been designing a coffee table made of bamboo for several months. the design costs will be approximately $5850. each table will cost $90 for material and labor. the company has decided to sell each table for 220 dollars.\ndefine units for the cost of production and the income obtained from the tables. enter a variable for the number of tables produced and use this variable to write expressions for the cost of production and the income obtained from the tables.\n1. what is the initial cost of production? what is the initial income?\n2. how much will the cost be and how much income would be obtained if 190 tables are produced?\n3. if the income was $39,600, how many tables were sold?

Answer

Explanation:

Step1: Define variables and cost - income expressions

Let $t$ be the number of tables produced. The design cost is a fixed cost of $$5850$, and the variable cost per table is $$90$. So the cost of production $C$ is given by the formula $C = 5850+90t$. The income $I$ from selling $t$ tables at $$220$ per table is $I = 220t$.

Step2: Find initial cost and income

When $t = 0$ (initial situation, no tables produced or sold): The cost of production $C(0)=5850 + 90\times0=5850$ dollars. The income $I(0)=220\times0 = 0$ dollars.

Step3: Calculate cost and income for $t = 190$

For cost: $C(190)=5850+90\times190=5850 + 17100=22950$ dollars. For income: $I(190)=220\times190 = 41800$ dollars.

Step4: Find number of tables sold given income

We know that $I = 220t$. If $I = 39600$, then $t=\frac{39600}{220}=180$ tables.

Answer:

  1. Initial cost of production: $$5850$, Initial income: $$0$.
  2. Cost when 190 tables are produced: $$22950$, Income when 190 tables are produced: $$41800$.
  3. Number of tables sold when income is $$39600$: 180 tables.