Question

Omnisport manufactures and sells sports equipment. It currently produces and sells 5,000 pairs (units) of in-line skates each year, operating at maximum machine capacity. Omnisport’s market research has revealed that it could sell 8,000 pairs of in-line skates annually. Calcott Inc., a nearby supplier, has offered to supply up to 6,000 pairs of in-line skates at a price of $75 per pair. However, Jack Petrone, Omnisport’s product manager, has noticed the current snowboarding craze and believes that Omnisport could sell up to 12,000 pairs (units) of snowboard bindings annually. Omnisport’s management accountant summarizes the available data: Manufactured Inline Skates (pair)		Snowboard Bindings (pair)		Purchased Inline Skates (pair)
Selling Price	$98		$60		$98
Cost per unit
Purchase cost	-		-		$75
Direct material	20		20		-
Variable machine operating cost ($16 per machine hour)	24		8		-
Variable and fixed manufacturing overhead (allocation base: machine hours)	18		6		-
Variable marketing and administrative cost	9		8		4

• Fixed manufacturing overhead costs of $30,000 are not affected by the product-mix decision.
• • Fixed manufacturing overhead costs are allocated to products based on a machine-hour rate, which is calculated by dividing total fixed manufacturing overhead costs of $30,000 by machine-hour capacity.
• • Fixed marketing and administrative costs of $60,000 are not affected by the product-mix decision.

Use Solver to determine the quantity of each product that Omnisport should manufacture and sell or purchased and sell to maximize operating income. What is the maximum operating income Omnisport can earn?

Answer 1

	As the Machine Hours are limited and the company is producing at 100% capacity we will have to see and find the optimal product mix where the operating income per machine hour is highest.
	Firstly, if we purchase the goods from Calcott Inc. then we would not be incurring any cost other than the fixed overhead which we will be incurring. For the purpose of decision making we will have to ignore the fixed cost as they are sunk cost and will have to be incurred irrespective of the fact whether the we produce in house or purchase from outside and hence the objective shall be to maximize the contribution (Sale Price-Varible Cost) per Machiner Hour (MHR). Hence we shall first calculate the Contribution per MHR we can earn by producing the skates and snowboard binding:
	Contribution per unit will be Rs. 19/Unit we will purchase the in-line skates as can be seen below:
	Sale Price - 98/Unit
	Purchase Price - 75/Unit
	Additional Variable Marketing & Administrative cost per unit - 4/Unit.
	Hence Contribution - 98-75-4=$19/Unit
	Contribution from Manufactured in-line skates
	Amount in $
	Molded plastic	8
	Other direct materials	12
	Variable machine operating costs ($16 per machine hour	24
	Marketing and administrative costs	9	53
	Sale Price Per Unit		98
	Contribution/Unit		45
	Total MHR Required for 1 Unit [ 24/ 16]		1.5 MHR
	Contribution/MHR		30/MHR
	Similarily we can calculate the Contribution/MHR for Snowboard bindings:
	Selling price per snowboard binding		$60
	Costs per snowboard binding
	Molded plastic	$16
	Other direct materials	4
	Variable machine operating costs ($16 per machine hour)	8
	Marketing and administrative costs	8	36
	Contibution per unit		$24
	Contibution per MHR (24*16/8)		$48/MHR
	now the optimal product mix will be where we can utilize the maximum capacity and ensure that the total operating income shall be highest.
	Currency Capacity - 5000 Units
	MHR Required/Unit - 1.50 Hrs ($ 24 being the machine variable operating cost @ 16/hour and hence total time - 1.5 hrs per unit)
	Hence Total Machine hours available is 7500 hours (5000units * 1.5hrs/unit)
	The total demand for snowboard binding is 12000 units and the time required for manufacturing 1 unit is half an hours and hence the total time required = 7500-(12000*0.50) = 1500 Hours.
	Hence the optimal product mix will be to
	1) Produce 12000 Units of Snowboard binding
	2) Produce 1000 Units of In-Line Skates
	3) Purchase 6000 Units of in-line skates from Calcott Inc
	Purchased 6000	Manufactured 1000 stakes	12000 snow boards	Total
Sales	$588,000	$98,000	$720,000	$1,406,000
Variable Cost
Direct Materials	$450,000	$20,000	$240,000	$710,000
Machine		$24,000	$96,000	$120,000
MOH		$12,000	$48,000	$60,000
Marketing	$24,000	$9,000	$96,000	$129,000
Contribution	$114,000	$33,000	$240,000	$387,000
Fixed Cost
MOH				$30,000
Marketing				$60,000
Operating Income				$297,000