Question

Answer In EXCEL

Best Plastics produces a line of cell phone covers. Its best-selling cover is the Cobra model, a
slim but very durable black plastic cover. The annual fixed cost for the Cobra model is $234,000.
This fixed cost includes management time, advertising, and other costs. In addition, the variable
cost, including labor and material costs, is $2 for each unit produced. Best Plastics sells the
Cobra for $3.50 per unit. The exact demand for next year is not known. Best Plastics wants to
analyze the possible profit against different quantities.
Define “q” as the quantity (number of units) required next year. Define TC(q) as the total cost to
manufacture q units. Define TR(q) as the total revenue from selling q units.
a. Write the algebraic equations for TC(q) and TR(q).

b. Define TP(q) as the total profit from selling q units, that is, TR(q) – TC(q). Write the
algebraic equation for TP(q).

Answer 1

We have the following information

Fixed Cost = $234,000

Variable cost per unit = $2

Total Cost equation: TC(q) = 234,000 + 2q, where q is the number of units produced

Total Revenue equation: TR(q) = Price × Quantity

TR(q) = 3.50q

Total Profit: TP(q) = TR(q) – TC(q)

TP(q) = 3.50q – 234,000 – 2q

TP(q) = 1.50q – 234,000

Quantity	Fixed Cost ($)	Variable Cost ($2 per unit)	Total Cost ($)	Price per unit ($)	Marginal Cost ($)
0	234000	0	234000	3.5	--
1	234000	2	234002	3.5	2
2	234000	4	234004	3.5	2
3	234000	6	234006	3.5	2
4	234000	8	234008	3.5	2
5	234000	10	234010	3.5	2
6	234000	12	234012	3.5	2
7	234000	14	234014	3.5	2
8	234000	16	234016	3.5	2
9	234000	18	234018	3.5	2
10	234000	20	234020	3.5	2
11	234000	22	234022	3.5	2
12	234000	24	234024	3.5	2
13	234000	26	234026	3.5	2
14	234000	28	234028	3.5	2
15	234000	30	234030	3.5	2
16	234000	32	234032	3.5	2
17	234000	34	234034	3.5	2
18	234000	36	234036	3.5	2
19	234000	38	234038	3.5	2
20	234000	40	234040	3.5	2