A small manufacturer of golf clubs is concerned about...

A small manufacturer of golf clubs is concerned about monthly costs. The workshop costs $\$ 23,250$ per month to run in addition to the $\$ 145$ in materials per set of irons produced. a. Write an equation for the monthly costs of this club manufacturer. b. What are the monthly costs for this company if they make 100 sets of irons? c. How many sets of irons does this manufacturer need to produce for their costs to be $\$ 20,000 ?$

A small manufacturer of golf clubs is concerned about monthly costs. The workshop costs $\$ 23,250$ per month to run in addition to the $\$ 145$ in materials per set of irons produced.
a. Write an equation for the monthly costs of this club manufacturer.
b. What are the monthly costs for this company if they make 100 sets of irons?
c. How many sets of irons does this manufacturer need to produce for their costs to be $\$ 20,000 ?$

Key Concepts

Linear Cost Function

A linear cost function represents the total cost as a sum of fixed costs and variable costs that change proportionally with the level of activity or production. In this context, the function is of the form Total Cost = Fixed Cost + (Variable Cost × Number of Units). This formula is fundamental in cost analysis and budgeting, enabling businesses to predict expenses based on production levels.

Fixed Costs

Fixed costs are expenses that remain constant regardless of the level of production or sales over a given period. They do not vary with how many units are produced. In cost modeling, fixed costs represent ongoing expenses that must be paid even when production is zero, such as rent or utilities.

Variable Costs

Variable costs change directly with the level of production; they increase as more units are produced and decrease when production declines. These costs are directly linked to the output level, such as the cost of raw materials or direct labor per unit. Understanding variable costs is essential for accurately modeling and controlling production expenses.

Equation Formulation

Formulating an equation in a cost problem involves defining the relationship between the number of units produced and the total cost incurred, taking into account both fixed and variable costs. This process typically starts by identifying the constant fixed cost and the per-unit variable cost, and then combining these to create a linear function that can be used for further analysis.

Solving Linear Equations

Solving linear equations involves algebraic manipulation to find unknown quantities, such as the number of units produced that results in a particular total cost. This technique is crucial in budgeting and production planning, enabling businesses to determine production levels that meet specific cost targets or constraints.

Transcript

00:01 When we're given the equation, y is equal to mx plus b, where we need to plug in values for m and b.

00:05 So m is always the rate.

00:06 This isn't something that happens per day, per month, per year, per person, something like that.

00:11 And then b is your initial value.

00:13 So for the situation here, we're talking about a golf club manufacturer.

00:16 It tells us that per month, there's workshop cost of $23 ,250.

00:22 And then we also have $145 in materials per set of iron.

00:27 So we're trying to figure out what the monthly cost is going to be.

00:30 Be for the manufacturer.

00:32 Now, even though it's happening per month, this is the amount that's going to be happening, and we're going to be coming up with a monthly equation.

00:39 So this is the initial amount.

00:40 Then we also have the information of the $145 per set of iris produced.

00:45 So there's no variables that are given, so we're going to go ahead and write the equation using y and x, but you can definitely use other variables instead.

00:52 So the m is the 145, so we have 145 times x, and then plus the initial value of the 23 ,250.

01:00 So now from here, we're going to answer part b, which wants to know what happens if we do 100 sets.

01:06 So what that means is we're going to plug in 100 for x, and we're going to solve this down...

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