1. The O\'Neill Shoe Manufacturing Company willp Assignment (Chapter 1, Part B)

Question

1. The O'Neill Shoe Manufacturing Company willp Assignment (Chapter 1, Part B) produce a special-style shoe if the production setup order, the size is large enough to prov'ide s 21000 for the produe company incurs a fixed cost of a reasonable profit. For each special setup. The variable cost is $50 per pair, and each pair sells for $70. the (a) Let z indicate the number of pairs of shoes prod model for the total cost of producing z pairs o of pairs of shoes produced. Develop a m total associated withe s produced. Develop a mathematical selling z pairs of shoes. C(r)- (b) Let r indicate the number of pairs of shoes model for the total revenue associated with selling r R(x)- (c) Let indicate the number of pairs of shoes model for the total profit realized from producing an ropo oducoed. Develop a mathematical selling r pairs of shoes. r P(z)- (d) What profit or loss can be anticipated with a demand of 50 pairs o (e) What proft or los can be anticipated with a demand of 200 pairs of shoes (0) Compute the number of pairs of shoes that should be made and sold to break pairs of even by setting the profit function equal to 0. (8) Use the following formula to compute the breakeven point. Breakeven point (Seling price per unit- Variable cost per unit) Fixed cost 2. Eastm an Publishing Company is considering publishing a paperback textbook on for business. The fixed cost of manuscript preparation, text- and production setup is estimated to be $160,000. Variable production pplications spre book design, material costs are estimated to be $10 per book. The publisher plans to sell the text to college and university bookstores for $50 each

Explanation / Answer

1. Fixed cost = $2000

Variable cost = $50

Selling cost = $70

a) cost function is given by

c(x) = fixed cost + (variable cost)(number of units produced)

= 2000 + 50x......(1)

Where x is the number of pairs of shoes produced.

b) revenue function is given by

R(x) = (selling cost)(number of pairs of shoes sold)

= 70.x ..........(2)

c) profit function is given by

P(X) = R(x) - C(x)

= 70x - ( 2000 + 50x)

= 20x - 2000.......(3)

d) for X= 50,

By equation (3), we get

P(X=50) = 20(50) - 2000

= -1000

So , there is loss on demand of 50 pairs of shoes.

e) for x =200

By equation (3), we get

P(X=200) = 20(200) - 2000

= $ 2000

So there is a profit on demand of 200 pairs of shoes

f) we need to calculate x at P(x) =0

By equation (3), we get

20x - 2000=0

x = 100.

So at 100 pairs of shoes, profit function becomes zero

g) using the formula given for breakeven point, we get

breakeven point = 2000/(70 - 50)

= 100

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