Question

SoundCo makes four different models of after-market radios for commercial trucks. Each radio model includes the base radio, a wiring harness, mounting bracket and mounting hardware. For each LD-1 model that SoundCo sells they generate revenue of $229, but incur costs of $89 for the base radio, $10 for a wiring harness, $8 for a mounting bracket, and $2 for mounting hardware. For each LD-2 model that SoundCo sells they generate revenue of $249, but incur costs of $89 for the base radio, $12 for a wiring harness, $10 for a mounting bracket, and $4 for mounting hardware. For each LD-3 model that SoundCo sells they generate revenue of $259, but incur costs of $99 for the base radio, $15 for a wiring harness, $14 for a mounting bracket, and $6 for mounting hardware. For each LD-4 model that SoundCo sells they generate revenue of $279, but incur costs of $109 for the base radio, $18 for a wiring harness, $20 for a mounting bracket, and $8 for mounting hardware. SoundCo management already has orders for 800 model LD-1 radios, and 700 model LD-3 radios that must be met. Management also decided that they will produce no more than 500 model LD-2 radios, as this model has not been popular with the company's customers. SoundCo has limited production capacity, and will not produce more than 2500 total radios. How many radios of each model does SoundCo produce that maximizes profit and meets their production constraints?

Answer 1

SoundCo

Units of radios to produce to maximize profit and meet production constraints:

LD-1 LD-2 LD-3 LD-4 Total

Units to be produced

to maximize profit 800 500 700 500 2,500

Explanation:

a) Data and Calculations:

LD-1 LD-2 LD-3 LD-4

Sales revenue $229 $249 $259 $279

Base radio cost $89 89 99 109

Wiring harness 10 12 15 18

Mounting bracket 8 10 14 20

Mounting hardware 2 4 6 8

Total costs $109 $115 $134 $155

Net Income $120 $134 $125 $124

Units to be produced

to maximize profit 800 500 700 500

First:

SoundCo must produce 800 and 700 units of LD-1 and LD-3 respectively to meet customer orders. Given that it has decided not to produce not more than 500 of LD-2, it is left with producing 500 of LD-4 because of the full capacity of 2,500.