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)

Correct answer iconYour answer is correct.

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

eTextbook and Media

  

Attempts: 1 of 3 used

  

(c)

Correct answer iconYour answer is correct.

What total contribution margin will Pharoah realize based on your answer to part (b)?

Total contribution margin

$enter the total contribution margin in dollars

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Attempts: 2 of 3 used

  

(d1)

Sarah has talked with the marketing department about the situation and suggested that the company raise the sales price on the weight bench to $64 to reduce customer demand. The marketing department believes that at the higher price, demand for the weight bench will drop to 5,920 units. How should Sarah allocate the 10,500 machine hours based on this new information?

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

Answer 1

Solution

Pharoah Innovations

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

So, total machine hours needed to produce enough units to meet the sales demand for the two products = 3,750 + 12,000 = 15,750

a. Allocation of available machine hours between the two products to maximize profits:

Allocation of machine hours would be as follows,

The product with highest contribution margin per machine hour should be first allocated the machine hours to meet the demand. The remaining hours are to be allocated to the product with the lowest contribution margin per machine hour.

Computation of contribution margin per machine hour –

Dumbbell Rack earns highest contribution margin per machine hour and hence ranked first.

The available machine hours are first allocated to Dumbbell Rack.

Available machine hours = 10,500

Market demand in units = 5,000

Machine hours needed to meet the demand for Dumbbell Rack = 5,000 units x 0.75 hours = 3,750

Remaining machine hours = 10,500 – 3,750 = 6,750

The remaining machine hours 6,750 are allocated for the production of weight bench.

Number of units of Weight Bench that can be produced using the remaining machine hours of 6,750 is = 6,750/1.50 = 4,500 units

Hence, Allocation of machine hours –

Dumbbell Rack - 3,750 machine hours

Weight Bench – 6,750 machine hours

Hence, the product mix to maximize profit with machine hours as the constraint is as follows,

Dumbbell Rack 5,000 units

Weight Bench 4,500 units

c. The total contribution margin based on answer in part (b) is as follows,

The maximum contribution at this product mix = (5,000 units x $17) + (4,500 units x $30) = $220,000

The total contribution margin using the available machine hours = $220,000

D1. Allocation of machine hours using the new information –

Computation of contribution margin per machine hour –

Since, Weight Bench earns highest contribution margin per mchine hour, the available hours are first allocated to Weight Bench.

Available machine hours 10,500

Sales demand for Weight Bench = 5,920 units

Machine hours needed for 5,920 units = 5,920 x 1.50 MH = 8,880

Remaining machine hours = 10,500 – 8,880 = 1,620

Number of units of Dumbbell Rack that can be produced using 1,620 machine hours = 1,620/0.75 = 2,160 units

Dumbell Rack       1,620 machine hours

Weight Bench       8,880 machine hours

Product mix –

Dumbbell Rack     2,160 units

Weight Bench       5,920 units

Maximum contribution margin at this mix –

Dumbbell Rack     2,160 x $17 = $36,720

Weight Bench       5,920 x $36 = $213,120

Total contribution margin = $249,840