Bernie Hsiao runs a lamp-making business. He has two lines of lamps: antler lamps and fishing rod lamps. It costs him $10,000 a year to run his business (labor, materials, and overhead). The estimated demand for antler lamps is anywhere from 100 to 200 units. The estimated demand for fishing rod lamps is 300 to 400 units. He charges $2000 for antler lamps and $200 for fishing rod lamps. However, he incurs $750 in variable costs per antler lamp sold and $30 for each fishing rod lamp sold.

a. What are Bernie’s expected/average revenues from antler lamps? What are Bernie’s expected/average revenues from fishing rod lamps? What is the total expected/average revenue Bernie’s lamp business could generate? What is the range of total expected/average profit?

b. What are the expected/average costs associated with the lamp business? Identify the costs associated with antler lamps, fishing rod lamps, and costs associated with both.

c. Does Bernie make a profit in the case of low estimated demand for each lamp?

d. Does Bernie make a profit in the case of high estimated demand for each lamp?

e. If half of the fixed costs are attributable to antler lamps, how much do the antler lamps contribute to this profit? If half the fixed costs are attributable to fishing rod lamps, how much do the fishing rod lamps contribute to this profit?

a) i) Expected revenue from Antler lamps

At Low Estimated Demand = 100 * 2000 = $200,000

At High Estimated Demand = 200 * 2000 = $400,000

Average revenue = (400000 + 200000)/2 = $300,000

ii) Expected revenue from Fishing rod lamps

At Low Estimated Demand = 300 * 200 = $60,000

At High Estimated Demand = 400 * 200 = $80,000

Average revenue = (60000 + 80000)/2 = $70,000

iii) Total expected revenue

At Low Estimated Demand = $200,000 + $60,000 = $260,000

At High Estimated Demand = $400,000 + $80,000 = $480,000

Average Total revenue = $260,000 + $480,000 = $370,000

iv) Total expected profit = Total revenue - total cost

At Low Estimated Demand = $260,000 - {(750*100) + (30*300) + 10000}

                                            =  $260,000 - $94000

                                            =  $166000

At High Estimated Demand = $480,000 - {(750*200) + (30*400) + 10000}

                                            =  $480,000 - $172,000‬

                                            =  $308,000

Range of profit = $166000 - $308,000

Average = $237,000‬

B) Expected cost with the business:

Fixed cost i.e. cost to run the business =  $10,000

Variable cost: At low demand for Antler lamps (750*100) = $75000

                       At high demand for Antler lamps (750*200) = $150000

                       At low demand for Fishing rod lamps (30*300) = $9000

                       At high demand for Fishing rod lamps (30*400) = $12000

Both: At low demand: $75000 + $9000 + $10,000 = $94000

        At high demand: $150000 + $12000 + $10,000 = $172,000‬

C) Yes, as illustrated in A)iv) there would be a profit of $166000

D) Yes, as illustrated in A)iv) there would be a profit of $308,000

E) Half fixed cost to Antler lamps:

At low demand: $200,000 - $75000 - $5000 = $120,000

At high demand: $400,000 - $150000 - $5000 = $245,000

Average = ($120,000 + $245,000)/2 = $182,5‬00

Half fixed cost to Fishing rod lamps:

At low demand: $60,000 - $9000 - $5000 = $46,000‬

At high demand: $80,000 - $12000 - $5000 = $63,000‬

Average = ($46,000‬ + $63,000‬)/2 = $54,5‬00

Step-by-step explanation:

Low Estimated Demand: Let 100 units be low demand for Antler lamps and 300 units be low for fishing rod lamps

High Estimated Demand: Let 200 units be high demand for Antler lamps and 400 units be high for fishing rod lamps

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x