The O\'Neill Shoe Manufacturing company will produce a special type of shoe if t

Question

The O'Neill Shoe Manufacturing company will produce a special type of shoe if the order size is sufficient to generate a reasonable profit. For each special-style order the company incurs a fixed cost of $1000 for the production set up. The variable cost is $30 per pair and each pair sells for $40.

Part A: Let x be the number of pairs of shoes produced. Write an expression for the total cost of producing x pairs of shoes.

Part B: Let R(x) denote the revenue hen x pairs of shoes are sold. Write an expression for the total revenue x pairs of shoes are produced.

Part C: Let P(x) the profit when x pairs of shoes are sold. Write an expression for the total profit when selling x pairs of shoes. Simplify your expression in the form P(x)=ax-b

Part D:

What is the profit when 120 pairs of shoes are sold and when 80 pairs of shoes are sold?

Complete the table:

Part E: What is the breakeven point (# pairs of shoes)?

Part F:

At the breakeven point the profit is

negative

positive

exactly zero

none of the above.

Part G:

If both fixed and variable manufacturing costs increased by 10% what would the new break-even point become? You need to recalculate the cost equation and set equal to revenue equation. Remember the context of this problem and what to do about rounding.

Explanation / Answer

part A) here total cost C(x) =fixed cost+variable cost

hence C(x) =1000+30x

part(B)  revenue R(X) =40x

part(C)  profit when x pairs of shoes are sold P(x) =R(x) -C(x) =40x-1000-30x =10x-1000

part (D) at x=120; profit P(120) =10*120-1000 =200

and at x=80; profit P(80) =10*80-1000 =-200 ; hence that would be a loss

part E ) break even point is when P(x) =0

hence 10x-1000=0

therefore x=100

part(f) exactly zero

part(g) as at break even point : revenue =fixed cost+varaible cost

hence 40x =1000*1.1 +30x*1.1

therefore (40-30*1.1)x =1000*1.1

x =1100/(40-33) =1100/7 =157.143

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