Question

Pharoah Innovations, Inc. produces exercise and fitness gear. Two of its newer products require a finishing process that can only be completed on machines that were recently purchased for this purpose. The machines have a maximum capacity of 10,500 machine hours, and no other products that the company makes use these machines.

Sarah Jacob, the company’s operations manager, is preparing the production schedule for the coming month and can’t seem to find enough machine time to produce enough units to meet the customer demand that the marketing department has included in the sales budget.

Michael Stoner, the company’s controller, has gathered the following information about the two products:

		Dumbbell Rack				Weight Bench
Selling price per unit			$44				$58
Direct materials			21				14
Direct labor			4				8
Variable overhead			2				6
Fixed overhead			4				10
Profit per unit			$13				$20
Unit sales demand			5,000				8,000
Machine hours per unit			0.75				1.5

(a)

Correct answer iconYour answer is correct.

Calculate the total number of machine hours needed to produce enough units to meet the sales demand for the two products.

Total number of machine hours

enter the total number of machine hours

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Attempts: 1 of 3 used

  

(b)

How should Sarah allocate the 10,500 available machine hours between the two products so that Pharoah maximizes its profits?

		Machine Hours
Dumbbell Rack		enter a number of machine hours
Weight Bench		enter a number of machine hours

Answer 1

(a)

Machine hours per unit of dumbbell rack = 0.75 hours

Unit sales demand of dumbbell rack = 5000 units

Machine hours per unit of weight bench = 1.5 hours

Unit sales demand of weight bench = 8000 units

• So the total machine hours need to produce enough units to meet the sales demand for the two product = (Unit sales demand of dumbbell rack*Machine hours per unit of dumbbell rack)+(Unit sales demand of weight bench*Machine hours per unit of weight bench)=(5000 units*0.75 hous)+(8000 units*1.5 hours)= 15750 hours

(b)

Maximum machine hours capacity = 10500 hours

The two product requires 15750 hours to meet the sales demand of the two product

So as we have a maximum capacity of 10500 hours the product which should be made first should be determined

To determine which product to be made first The product which makes the highest contribution per machine hours will be made first

Dumbbell rack

Selling price per unit=$44

Direct materials=$21

Direct Labour=$4

Variable overhead=$2

Machine hour per unit= 0.75

Contribution per unit of dumbbell rack = Selling price-Direct material cost per unit-Direct labour cost per unit-Variable overhead per unit= $44-$21-$4-$2=$17 per unit

• Contribution per machine hours of dumbbell rack=Contribution per unit/Machine hour per unit =$17/0.75 hours = $22.66666667 per machine hour

Weight bench

Selling price per unit=$58

Direct materials=$14

Direct Labour=$8

Variable overhead=$6

Machine hour per unit= 1.5 hours

Contribution per unit of Weight bench = Selling price-Direct material cost per unit-Direct labour cost per unit-Variable overhead per unit=$58-$14-$8-$6=$30 per unit

• Contribution per machine hours Weight bench=Contribution per unit/Machine hour per unit = $30/1.5 hours per unit= $20 per machine hour

So as the Dumbbell rack have a higher contribution per machine hour Dumbbell rack will be produced 1st

And Weight bench will be produced 2nd

Dumbbell rack unit sales demand= 5000

Machine hour per unit=0.75

As the maximum capacity is 10500 hours

10500 hours is to be allocated Inorder to maximize its profit the allocation is

• Total machine hours to be allocated to Dumbbell rack = 5000 units*0.75= 3750 hours
• Total machine hours to be allocated to weight bench = 10500 hours-(Total machine hours allocated to Dumbbell rack) = 10500 hours-3750 hours = 6750 hours