13. assume that cane’s customers would buy a maximum of 80,000 units of alpha and 60,000 units of beta. also assume that the raw material available for production is limited to 160,000 pounds. how many units of each product should cane produce to maximize its profits?

80000 unit of Alpha

Explanation:

This is a Limiting factor/resource constraint question. In certain situations entities suffer from shortage of necessary resources (e.g: shortage of material, labor hours, machine hours), in such circumstances entities strive to allocate the constraint resources to the production of those products which generate the highest contribution per limiting factor and help maximize total contribution. In this case the limiting factor for Cane is Raw material.

Lets suppose that each unit of Alpha and Beta sell for $120 and $80 respectively and variable cost per unit of Alpha and Beta is $69 and $20 respectively. Each unit of Alpha and Beta require 2 and 5 pounds of raw material for production respectively.

Now that we have supposed the data we have to compute contribution per unit and then contribution per limiting factor and based on the ranking (i.e highest first) of contribution per limiting factor we decide which product should be given priority for resource allocation.

Lets calculate contribution per unit.

Alpha:

Contribution per unit= SP-VC

Where, SP stands for selling price and VC stands for variable cost.

CPU= 120-69

CPU=$51

Beta:

Contribution per unit= 80-40

CPU=$40

Now, lets calculate contribution per limiting factor.

Alpha:

CLF: $51÷2

CLF: $25.5        1st Rank

Beta:

CLF: $40÷5

CLF: $8              2nd Rank

So clearly Alpha has a greater contribution per limiting factor and it implies that Alpha will earn the highest contribution margin therefore Cane should produce and allocate resources to Alpha first and then Beta if there remains any?

Profit maximizing output:

It requires 2 pounds of raw material to produce one unit of Alpha (i.e 80000×2=160000) Therefore Cane should produce 80000 units of Alpha only in order to maximize its profits.

i think this is true i hope this