Q35. - Algebra 2

Question

There are a total of   workers hours available per day for production at a calculator manufacturer. There are   workers hours variable for encasement and Quality Control each day. The table below shows the number of hours needed in each department for two different types of Calculators.

35. Determine the number of each type of calculator that is needed to make maximum profit.

Step-by-Step Solution

Answer

Number of graphing calculator =0 

Number of CAS calculator  =85

For maximum profit

Step-1 –Determination of maximum value

The co-ordinates of A,B,C,D are $A(0,85),B(0,80),C(20,0),D(\frac{173}{3},0)$

$P=50g+65c$

At point  $A(0,85)$

$\begin{array}{c}P=65\times 85\\ =5525\end{array}$

At point  $B(0,80)$

$\begin{array}{c}P=65\times 80\\ =5200\end{array}$

At point  $C(20,0)$

$\begin{array}{c}P=50\times 20\\ =1000\end{array}$

At point $D(\frac{173}{3},0)$

$\begin{array}{c}P=50\times \frac{173}{3}\\ =2883.33\end{array}$

Step 2: Identify the algebraic structure

Determine the type of algebraic problem.

Step 3: Apply algebraic techniques

Use factoring, expanding, or systematic methods.

Step 4: Simplify and solve

Simplify expressions and solve for unknowns.

Step 5: State the result

Write the final answer.

Step 6: Conclude with the answer

Number of graphing calculator =0 

Number of CAS calculator  =85

For maximum profit