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QuestionA company makes smartphones A and B. Find break-even points, optimal production for max profit, and total profit for 1,000 units.

Studdy Solution

STEP 1

Assumptions1. The production cost for Model A is 150perunit.ThesellingpriceforModelAis150 per unit. The selling price for Model A is 250 per unit3. The production cost for Model B is 200perunit4.ThesellingpriceforModelBis200 per unit4. The selling price for Model B is 300 per unit5. The company has a production capacity of1,000 units6. The break-even point is the number of units that need to be sold to cover the production costs7. The company wants to maximize its profit

STEP 2

First, let's find the profit per unit for each model. The profit per unit is the selling price minus the production cost.
Profit per unit=Selling price−Production costProfit\, per\, unit = Selling\, price - Production\, cost

STEP 3

Now, plug in the given values for the selling price and production cost for Model A to calculate the profit per unit.
Profit per unit A=$250−$150Profit\, per\, unit\, A = \$250 - \$150

STEP 4

Calculate the profit per unit for Model A.
Profit per unit A=$250−$150=$100Profit\, per\, unit\, A = \$250 - \$150 = \$100

STEP 5

Similarly, plug in the given values for the selling price and production cost for Model B to calculate the profit per unit.
Profit per unit B=$300−$200Profit\, per\, unit\, B = \$300 - \$200

STEP 6

Calculate the profit per unit for Model B.
Profit per unit B=$300−$200=$100Profit\, per\, unit\, B = \$300 - \$200 = \$100

STEP 7

Now, let's find the break-even point for each model. The break-even point is the production cost divided by the profit per unit.
Break−even point=Production cost/Profit per unitBreak-even\, point = Production\, cost / Profit\, per\, unit

STEP 8

Plug in the values for the production cost and profit per unit for Model A to calculate the break-even point.
Break−even point A=$150/$100Break-even\, point\, A = \$150 / \$100

STEP 9

Calculate the break-even point for Model A.
Break−even point A=$150/$100=.5Break-even\, point\, A = \$150 / \$100 =.5

STEP 10

Similarly, plug in the values for the production cost and profit per unit for Model B to calculate the break-even point.
Break−even point B=$200/$100Break-even\, point\, B = \$200 / \$100

STEP 11

Calculate the break-even point for Model B.
Break−even point B=$200/$100=Break-even\, point\, B = \$200 / \$100 =

STEP 12

Since the company cannot produce fractional units, the break-even points for Model A and Model B are2 and2 units respectively.

STEP 13

Now, let's find out how many units of each model the company should produce to maximize its profit. Since the profit per unit for both models is the same, the company should produce as many units as possible.

STEP 14

Given the company's production capacity of,000 units, the company should produce500 units of Model A and500 units of Model B to maximize its profit.

STEP 15

Finally, let's calculate the total profit the company would make if they follow this production plan. The total profit is the number of units produced times the profit per unit.
Total profit=Number of units producedtimesProfit per unitTotal\, profit = Number\, of\, units\, produced \\times Profit\, per\, unit

STEP 16

Plug in the values for the number of units produced and the profit per unit for Model A to calculate the total profit.
Total profit A=500times$100Total\, profit\, A =500 \\times \$100

STEP 17

Calculate the total profit for Model A.
Total profit A=500times$100=$50,000Total\, profit\, A =500 \\times \$100 = \$50,000

STEP 18

Similarly, plug in the values for the number of units produced and the profit per unit for Model B to calculate the total profit.
Total profit B=500times$100Total\, profit\, B =500 \\times \$100

STEP 19

Calculate the total profit for Model B.
Total profit B=500times$100=$50,000Total\, profit\, B =500 \\times \$100 = \$50,000

STEP 20

Add the total profits for Model A and Model B to find the overall total profit.
Overall total profit=Total profit A+Total profit BOverall\, total\, profit = Total\, profit\, A + Total\, profit\, B

STEP 21

Plug in the values for the total profit for Model A and Model B to calculate the overall total profit.
Overall total profit=$50,000+$50,000Overall\, total\, profit = \$50,000 + \$50,000

STEP 22

Calculate the overall total profit.
Overall total profit=$50,000+$50,000=$100,000Overall\, total\, profit = \$50,000 + \$50,000 = \$100,000The company would make a total profit of $100,000 if they produce500 units of Model A and500 units of Model B.

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