Question

Layton Machining Company (LMC) manufactures two versions of a basic machine tool. One version is a standard model and one is a custom model, which requires some additional work and slightly higher-grade materials. The manufacturing process at LMC requires that each product go through two departments, Grinding and Finishing. The process in each department uses a single type of machine. Total machine capacity in Grinding is 77,000 hours, and in Finishing, total machine capacity is 57,500 hours. (Each department has multiple machines.) Total market demand is limited to 154,000 standard units and 174,000 custom units monthly. LMC is currently producing 144,000 standard units and 106,000 custom units each month. Cost and machine-usage data for the two products follow:

	Standard			Custom			Total
Price	$	7.70		$	9.70
Less variable costs per unit
Material		2.00			2.50
Labor		1.75			2.00
Overhead		2.25			3.00
Contribution margin per unit	$	1.70		$	2.20
Fixed costs
Manufacturing							$	86,000
Marketing and administrative								47,000
							$	133,000
Grinding machine hours per unit		0.2			0.3
Finishing machine hours per unit		0.1			0.4
Grinding machine hours used								60,600
Grinding machine hours available								77,000
Finishing machine hours used								56,800
Finishing machine hours available								57,500
Quantity produced		144,000			106,000
Maximum demand		154,000			174,000
Profit	$	345,000

Required:

a. What is the optimal production schedule for LMC? In other words, how many standard units and custom units should the company produce each month to maximize monthly profit?

b. If LMC produces at the level found in requirement (a), how much will monthly profit increase over the current production schedule?

Answer 1

Please find below table useful to compute desired results: -

C. 1 9.7 -D15 H Standard Custom Total Calculation of Maximum unit of Custom Grinding Finishing 2 Price 7.7 Hours Available =D17 3 Less variable costs per unit Hours Required for producing standard units |=B19*B12 =B19*B13 4 Material Balance Hours available for custom =G2-G3 =H2-H3 5 Labor Hours required to produce 1 unit of custom 1-C12 =C13 6 Overhead Maximum unit that can be produced =G4/G5 FH4/H5 7 Contribution margin per unit *Priority should be to meet maximum demand of standard units 8 Fixed costs The optimal Production Schedule for LMC is 9 Manufacturing 86000 Standard Units =B19 i.e. Maximum demand 10 Marketing and administrative 47000 Custom Units =H6 Computed above 11 133000 12 Grinding machine hours per unit Calculation of Monthly profit increase: - 13 Finishing machine hours per unit Particulars Standard Units Custom Units Total 14 Grinding machine hours used 60600 Hours Available =G9 =G10 15 Grinding machine hours available 77000 Contribution margin per unit =B7 =C7 16 Finishing machine hours used 56800 Total Contribution =G14*G15 =H14*H15 =G16+H16 17 Finishing machine hours available 57500 Less: Fixed Cost 18 Quantity produced 144000 106000 Manufacturing =D9 19 Maximum demand 154000 174000 Marketing and administrative =D10 20 Profit 345000 Total fixed costs =118-119 21 Profit =116-120 Determination of the contribution Margin per machine hour Less: Current profit =B20 23 Grinding Finishing Monthly profit increase =121-122 24 Particulars Standard Units Custom Units Standard Units Custom Units 25 Contribution Margin per unit =B7 =C7 =B7 =C7 26 Grinding Machine Hours required to produce 1 Unit |=B12 =C12 =B13 =C13 27 Contribution Margin per machine Hour =B25/B26 =C25/C26 =D25/D26 =E25/E26 22

End results would be as follows: -

H Calculation of Maximum unit of Custom Grinding Finishing Hours Available 77.000.00 57.500.00 Hours Required for producing standard units 30,800.00 15,400.00 Balance Hours available for custom 46,200.00 42,100.00 Hours required to produce 1 unit of custom 0.30 0.40 Maximum unit that can be produced 154,000.00 105,250.00 *Priority should be to meet maximum demand of standard units The optimal Production Schedule for LMC is Standard Units 154,000.00 i.e. Maximum demand Custom Units 105,250.00 Computed above Total 1 Standard Custom Total 2 Price 7.70 9.70 3 Less variable costs per unit 4 Material 2.00 2.50 5 Labor 1.75 2.00 6 Overhead 2.25 3.00 7 Contribution margin per unit 1.70 2.20 8 Fixed costs 9 Manufacturing 86,000.00 10 Marketing and administrative 47,000.00 11 133,000.00 12 Grinding machine hours per unit 0.20 0.30 13 Finishing machine hours per unit 0.10 0.40 14 Grinding machine hours used 60,600.00 15 Grinding machine hours available 77,000.00 16 Finishing machine hours used 56,800.00 17 Finishing machine hours available 57,500.00 18 Quantity produced 144,000.00 106,000.00 19 Maximum demand 154,000.00 | 174,000.00 20 Profit 345,000.00 21 22 Determination of the contribution Margin per machine hour 23 Grinding Finishing 24 Particulars Standard Units Custom Units Standard Units Custom Units 25 Contribution Margin per unit 1.70 2.20 1.70 2.20 26 Grinding Machine Hours required to produce 1 Unit 0.20 0.30 0.10 0.40 27 Contribution Margin per machine Hour 8.50 7.33 17.00 5.50 493,350.00 Calculation of Monthly profit increase: - Particulars Standard Units Custom Units Hours Available 154,000.00 105,250.00 Contribution margin per unit 1.70 2.20 Total Contribution 261,800.00 231,550.00 Less: Fixed Cost Manufacturing Marketing and administrative Total fixed costs Profit Less: Current profit Monthly profit increase 86,000.00 47,000.00 133,000.00 360,350.00 345,000.00 15,350.00