Question

Question 1. Tom Johnson Manufacturing intends to increase the capacity through the addition of new equipment. Two vendors have presented proposals. The fixed cost for proposal A is $95000 and for propos $10 and for B, $12. The revenue generated by each unit of A is al B is $80,000. The variable cost for A is $50 and B is S60. (Hints: Interpret proposal A as product A; a) What is the breakeven point in units and in dollars for b) What is the breakeven point in units and in dollars for proposal B as product B) proposal A? proposal B? be chosen? Provide your rea of A by $50,000. In order to satisfy this condition, how c) If the expected volume is 7800 units, which proposal should son with evidence For a specific sales volume, proposal B is higher than profit many units should be sold? Question 2. A doctor prescribes a sick freshman fruits (Banana and Orange) that provide Vitamin A, Vitamin B and Vitamin C A pound of Banana contributes 8 grams of Vitamin A and 6 grams of Vitamin B and 2 grams of Vitamin C while a pound of Orange contributes 2 grams of Vitamin A and 6 grams of Vitamin B. A pound of Banana costs S4 and a pound of Orange costs $6. The student has to meet a minimum requirement of 27 grams of Vitamin A, 38 grams of Vitamin B and 6 grams of Vitamin C. The student should avoid taking more than 53 grams of Vitamin A and 71 grams of Vitamin B to avoid side effects such as nausea and vomiting. The pounds of banana eaten should be more than the pounds of orange eaten by at least 2 pound. Formulate a linear programming problem to help the poor freshman to choose the fruit mix to recover fast.

Answer 1

Solution

Back-up Theory

BREAK-EVEN ANALYSIS

Terminology

F = Fixed cost, v = Variable cost per unit, T = Total cost, r = Revenue per unit, R = Total revenue,

p = Profit per unit, P = Total profit, x = Number of units.

Then,

T = F + vx ……………………………………………………………………………………… (1)

R = rx …………………………………………………………………………………………… (2)

P = R – T = rx - (F + vx) = x(r - v) - F…………………………………………………...…… (3)

Break-even units is that value of x at which P = 0, i.e., x(r - v) = F or x = F/(r - v) .……..(4)

Break-even value = xr = rF/(r - v), where x is the break-even units ……………...………(5)

Now to work out the solution,

Part (a)

Product (Proposal) A

Given F = 95000, v = 10, r = 50, vide (4),

Break-even units, x = 95000/40 = 2375 Answer 1

vide (5),

Break-even value, rx = 50 x 2375 = $118750 Answer 2

Part (b)

Product (Proposal) B

Given F = 80000, v = 12, r = 60, vide (4),

Break-even units, x = 80000/48 = 1666.67 = 1667 Answer 3

vide (5),

Break-even value, rx = 60 x (80000/48) = $100000 Answer 4

Part (c)

Given proposed volume, i.e., x = 7800, vide (3)

Profit for A = (7800 x 40) – 95000 = $217000

Profit for B = (7800 x 48) – 80000 = $294400

Clearly, Profit for B > Profit for A and hence Proposal B must be chosen   Answer 5

Part (d)

Let x* be the number of units at which profit for B is higher than that for A by 50000,

=> (Profit for B - Profit for A) > 50000

i.e., vide (3), {(48x* - 80000) - (40x* - 95000)} > 50000

or 8x* > 35000

or x* > 4375

Thus, profit for B is higher than that for A by 50000 when the volume is at least 4376. Answer

DONE