Management Science Assignment number 6 PDF

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Navarro Trixie T.

Assignment #6

PCBET 01-601P

Management Science

1. A small-scale industry sells its products at P2.80 per unit. The variable cost is P1.80 per unit. The total fixed cost is P20,000. Determine the following:

a. The break-even quantity and revenue Break-even quantity = Fixed cost/Selling price – Variable cost = 20,000/2.8-1.8 = 20,000/1 Break-even quantity = 20,000 Revenue = Selling price x break-even quantity = 2.8 x 20,000 Revenue = 56,000

b. The profit (or loss) at a sales volume of P15,000 units Cost = 20,000 + (1.8) (15,000) Cost = 20,000 + 27,000 Cost = 47,000

Selling price = 2.8 x 15,000 = 42,000 Loss = 47,000-42,000 Loss = 5,000

c. How can profit be generated if there is a loss in (b) Profit is generated when selling price > Cost price 2.8 units > 20,000 + 1.8 units 2.8 – 1.8 > 20,000 unit > 20,000 When the number of sold is greater than 20,000, then the profit is generated.

d. Up to how much should the selling price per unit be increased or decreased to break-even at 15,000, assuming that FC and UVC remain constant. 20,000 + 1.8 x 15,000 = unit (15,000) 20,000 + 27,000 = unit (15,000) 15,000 unit = 47,000 Unit = 47,000/15,000 Unit = 3.133 Selling price = 3.133

2. A small-scale manufacturer can sell Q number of units of each product produced per week at a price of (18 – 0.02q) pesos. It costs P8 to make each unit of the product. The fixed cost associated with producing and selling the product weekly is P450. Determine: a. The TR, TC and profit Function. TR = (18 – 0.02q)q TR = 18q – 0.02q2 TR = - 0.02q2 + 18q TC = 8q + 450 P = -0.02q2 + 18q -8q – 450

P = -0.02q2 + 10q – 450

b. Production level to break-even. At BEP, P = 0; TR = TC -

0.02q2 + 18q = 8q + 450

-

0.02q2 + 10q – 450 = 0

−¿ +¿√b 2−4 ac/2a −b¿ q=¿ −¿ +¿√(10) 2−4(−0.02)(−450/ 2(−0.02) −10¿ q=¿ q= −10± 8 /−0.04 q= −2 /−0.04 =50 units q= -18/-0.04 =450 units

c. Production level to maximize profit. P ’ = -0.04q + 10 0.04q = 10 q = 250 units d. Maximum profit at this level. Pmax = -.02(250)2 + 10(250) -450 = P800 e. Interpret the meaning of the two break-even points There are two break-even points: (50, 450). This means that selling less than 50 as well as selling more than 450 units would mean a loss for the company....