Lighting Warehouse produces [tex]q[/tex] solar lamps at a fixed cost of [tex]R 60000[/tex] per week. Each lamp costs [tex]R 30[/tex].

What are the equations for total revenue, total cost, and profit function?

A. [tex]T R = 600q; T C = 300q + 60000;[/tex] profit [tex]= 900q + 60000[/tex]

B. [tex]T R = 300q + 60000; T C = 600q;[/tex] profit [tex]= -300q + 60000[/tex]

C. None of the given options is correct.

D. [tex]T R = 600q; T C = 300q + 60000;[/tex] profit [tex]= 300q - 60000[/tex]

E. [tex]T R = 600q; T C = 300q;[/tex] profit [tex]= 300q[/tex]

Let's break down the problem step by step:

1. First, we determine the total revenue. Since each lamp is sold for R600, if the company sells [tex]$q$[/tex] lamps then the total revenue [tex]$TR$[/tex] is given by

[tex]$$
TR = 600q.
$$[/tex]

2. Next, we calculate the total cost. The cost has two parts:
- The variable cost: Each lamp costs R300 to produce, so for [tex]$q$[/tex] lamps the variable cost is [tex]$$300q.$$[/tex]
- The fixed cost: There is a fixed cost of R60000 per week.

Therefore, the total cost [tex]$TC$[/tex] is:

[tex]$$
TC = 300q + 60000.
$$[/tex]

3. Finally, the profit is the total revenue minus the total cost. Thus, the profit [tex]$P$[/tex] is:

[tex]$$
\text{Profit} = TR - TC = 600q - (300q + 60000).
$$[/tex]

Simplify the expression:

[tex]$$
\text{Profit} = 600q - 300q - 60000 = 300q - 60000.
$$[/tex]

To summarize, we have:
- Total Revenue: [tex]$$TR = 600q,$$[/tex]
- Total Cost: [tex]$$TC = 300q + 60000,$$[/tex]
- Profit: [tex]$$P = 300q - 60000.$$[/tex]

Comparing these results with the provided options, the correct answer is:

d. [tex]$$TR = 600q; \quad TC = 300q + 60000; \quad \text{Profit} = 300q - 60000.$$[/tex]